Envision Math Grade 8 Volume 1 Chapter 2 Analyze And Solve Linear Equations
Page 141 Exercise 1 Answer
Given
statement
To find/solve
Construct an argument to defend Xiu’s statement.
A y-intercept or vertical intercept is a point where the graph of a function or relation intersects the y-axis of the coordinate system. These points satisfy x = 0.
Xiu stated correctly that they passed the one-mile mark couple of minutes ago because they did not start from the sea level, but were already 2,080 ft above the sea level.
The starting height was 2,080 ft, so Xiu is correct.
The starting height was 2,080 ft, so Xiu is correct.
A y-intercept or vertical intercept is a point where the graph of a function or relation intersects the y-axis of the coordinate system. These points satisfy x=0.
Jon knew that the Mountain Tram is moving at 800 vertical ft/min and multiplied that by the minutes that are needed to reach the 1 mile point. We know that
1 mile is equal to 5,280 ft.
Now we get,
800 × 6.5 = 5200
He was correct about that part but forgot that they started at 2,080 ft above the sea level.
He forgot that they started at 2,080 ft above the sea level.
He forgot that they started at 2,080 ft above the sea level.
Page 141 Exercise 1 Answer
We need to find whether there is a proportional relationship between x and y.
Also, check whether the equation y = mx represents the path of the tram or not.
We can partly use given equation y = mx because the tram starts moving from 2,080ft above the sea level and that must be added to the equation.
So now the new equation would look something like y = mx + b
We can use it but have to add the starting value to the equation.
Thus, there won’t be any proportional relationships that exists.
This is because the value of y depends on the value of both x and b
We can use the equation y = mx but we have to add the starting value to the equation. i.e., y= mx + b
There is NO proportional relationship between x and y since the value of y changes corresponding to both x and b.
Page 142 Exercise 1 Answer
Given
To find/solve
Write a linear equation in slope-intercept form.
First, we have to look at the y-intercept to find out from which value has the graph started.
The y-intercept is 2
Secondly, we have to find the slope of the given line. To find the slope we are going to use two points on the graph that we can read which are (4,5) and (8,8).
Now the equation is y = 0.75x + 2.
Hence, the y-intercept is 2
and the slope is 0.75
The equation is y = 0.75x + 2.
Page 143 Exercise 2 Answer
Given
To find/solve
What is an equation for the line shown.
First, we have to find the y-intercept of the given line.
The y-intercept is 2.
Secondly, we have to find the slope of the given line. We have to use two points which are (4,0) and (0,2)
The equation is y = -0.5x + 2.
The equation is y = -0.5x + 2.
Given
To find/solve
Graph the line.
When we look at the equation of given line we can see that it has -5. This means that the y-intercept is -5.
The slope of given line is 1/3.
We have to find the y-intercept and the slope first, and simply graph the line after that.
We have to find the y-intercept and the slope first, and simply graph the line after that.
Page 144 Exercise 1 Answer
Given
Statement
To find/solve
Equation of a line.
A y-intercept or vertical intercept is a point where the graph of a function or relation intersects the y-axis of the coordinate system. These points satisfy x = 0.
The equation for a line of a non proportional relationship is y = mx + b
where m is the slope and b is the y-intercept.
The equation is y = mx + b
The equation is y = mx + b
Page 144 Exercise 4 Answer
Given
To find/solve
Which student is correct.
A y-intercept or vertical intercept is a point where the graph of a function or relation intersects the y-axis of the coordinate system. These points satisfy x=0.
First we look at the graph to see what is the y-intercept.
The y- intercept is 5.
Now that we have found the intercept we can see that the line is decreasing which means that the slope is negative.
George is correct.
Hence, we found out that George is correct.
Page 144 Exercise 5 Answer
Given
To find/solve
Draw a line to show the relationship between the number of hours the tent is rented, x, and the total cost of the tent,y
Since we know that the set-up fee is $100 then we know that this will be our y-intercept.
The cost per hour is additional $500. This is the slope of given equation. Now we can write whole equation.
y = 500x + 100
Now the graph is obtained by adding 100 to the variable then the graph of given equation will be translated 100 units up on the y-axis.
We have to find the equation of given line which is y = 500x + 100 and after that simply graph that line.
We have to find the equation of given line which is y = 500x + 100 and after that simply graph that line.
Given
To find/solve
What is the equation of the line in slope-intercept form?
To find the equation first we have to see the data that we are given in the task. Since it states that the cost of the tent is $500 per hour, that means that this will be our variable.
The set-up fee is in for every tent and it is a one-time pay per tent. This means that we have to add the $100 to the variable.
Now we know how our equation will look like
y = 500x + 100
The equation is y = 500x + 100.
The equation is y = 500x + 100.
Page 145 Exercise 6 Answer
Given
We need to find the y-intercept of the given equation y = 2x + 4. Also, find another point using the slope of the line and daw a line to connect the two points.
If we look at the equation we can see that we have added 4 to the variable and that means that the y-intercept will be 4. The point at which the line will cross y-axis is (0,4).
The slope is positive and that means that the graph will be increasing from left to right.
We will simply start at the y-intercept and move up to 2 points and then we will move 1 point to the right.
Draw a line through points (0,4) and (1,6). This is the line of the given equation.
Graph the given equation and draw a line to connect the obtained two points.
The y -intercept is 4, which means the line crosses the y -axis at the point (0,4)
The slope of the line is positive, so it goes increasing from left to right.Start at the y-intercept. Move up 2units, and then move right 1unit.
You are now at the point (1,6)
Graphing the given equation and plotting the points, we get,
Page 145 Exercise 7 Answer
Given
To find/solve
Write an equation.
We have to use two points from the graph that are visible and one of them will be the y-intercept (0,-3)
The other point we are going to use is (2,-4).
Now to find the slope.
The equation is y = -0.5x – 3
The equation is y = -0.5x – 3
Page 145 Exercise 8 Answer
Given
To find/solve
Write an equation.
We have to use two points from the graph that are visible and one of them will be the y-intercept (0,4)
The other point we are going to use is (-1,1).
Now to find the slope.
The equation is y = 3x + 4
The equation is y = 3x + 4
Page 145 Exercise 9 Answer
Given
To find/solve
Write an equation.
If we look at the kayak rentals in the task we can see that the cost per hour is $12, and that will be our variable.
As for the $6 deposit, that will happen only once every time someone rents a Kayak.
Now the equation is y = 12x + 6
The equation is y = 12x + 6.
Page 145 Exercise 10 Answer
Given
To find/solve
Graph the equation y = 3x − 5.
In order to graph the given equation, we have to know the slope of the given equation, and they-intercept.
Since we know the y-intercept. We got the one point of the graph which is 0,−5.
Then if we need another equation to draw the graph when the y-coordinate is 0.
0 = 3x − 5
3x = 5
\(x=\frac{5}{3}\)The graph becomes,
The two points are (0,−5)and (5/3,0).
The two points are(0,−5) and (5/3,0).
The graph is,
Page 146 Exercise 11 Answer
Given
To find/solve
What is the correct equation.
Since we know that she had $25 in her bank account at start that means that the y-intercept is in point (0,25). Then the y-intercept is 25
Then she spends $5 every day this means the variable is subtracted by -5
Then the equation is y = −5x + 25.
Then the equation is y = −5x + 25.
Given
To find/solve
What mistake might Amy have made.
Amy has added only $5 to the variable and that would mean that she had $5 in her account on the start.
This means that she must have used the positive value of slope for the y-intercept as well.
She might have used the positive value of slope as y-intercept.
She might have used the positive value of slope as y-intercept.
Page 146 Exercise 12 Answer
Given
Graph
To find/solve
Write an equation for the line in slope intercept form.
From the graph we get the slope and y-intercept to write the equation.
The y-intercept is 12.25 and then means that we have to add that value to the variable.
To find the slope,
We know that each ticket cost $21, then it will be our slope.
The equation is y = 21x + 12.25
The equation is y = 21x + 12.25
Given
To find/solve
write an equation.
We can write the equation by reading the part where they show us the price of each ticket and the processing fee for each transaction.
As we can see the processing fee will be paid each transaction once and the price of each ticket will be $21, which means that we can order multiple that would give us the equation.
y = 21x + 12.25 which is the same as in the first part of the task.
We have the picture in the task which shows us the price of each ticket and the processing fee for each transaction.
We have the picture in the task which shows us the price of each ticket and the processing fee for each transaction and the equation is y = 21x + 12.25
Given
Graph
To find/solve
Is this graph a good representation of the situation.
Give graph would be a good representation of the situation if no one would buy more than 4 tickets.
Since the line of the graph is shown to the number of 4 tickets, we do not know from the graph how much will we have to pay for more than 4 tickets.
The graph is a good representation if we no one buys more than 4 tickets.
The graph is a good representation if we no one buys more than 4 tickets.
Page 146 Exercise 13 Answer
Given
Graph the equation \(y=\frac{2}{5} x-1\)
To find/solve
What should you do first to graph the equation.
A y-intercept or vertical intercept is a point where the graph of a function or relation intersects they-axis of the coordinate system. These points satisfy x = 0.
When we have to graph some equation, then the first thing we want to do is to mark the y-intercept. This will show us where the graph of the line will begin.
Plot a point at the y-intercept.
Plot a point at the y-intercept.
Page 146 Exercise 14 Answer
Given
To find/solve
Write an equation for the line in slope-intercept form.
First, we want to find the y-intercept of the given line. As we can see from the graph the point of the y-intercept is (0,8).
This means that the y-intercept is 8.
Secondly, we want to find the slope of the given line. To do this we have to use two points from the graph that we can read. The first point is going to be the y-intercept and the second will be the x-intercept, which is (4,0).
The equation of the line is y = -2x + 8
The equation of the line is y = -2x + 8