Envision Math Grade 8 Volume 1 Chapter 5 Analyze And Solve System Of Linear Equations
Page 255 Exercise 2 Answer
Given: When lines are the same distance apart over their entire lengths, they are _____________________ .
To find: Choose the best term from the box to complete each definition.
Parallel lines are lines in a plane that do not intersect at any point; for example, two straight lines in a plane that do not collide at any point are said to be parallel. Curves that do not touch or intersect and maintain a constant minimum distance are considered to be parallel.
When lines are the same distance apart over their entire lengths, they are parallel.
Page 255 Exercise 4 Answer
Given: A _________ is a relationship between two variables that gives a straight line when graphed.
To find: Choose the best term from the box to complete each definition.
Linear equations are nothing but yet another subset of “equations”. Any linear calculations requiring more than one variable can be done with the help of linear equations. The standard form of a linear equation in one variable is of the form ax + b = 0. Here, x is a variable, and a and b are constants. While the standard form of a linear equation in two variables is of the form ax + by = c. Here, x and y are variables, and a, b and c are constants.
A linear equation is a relationship between two variables that gives a straight line when graphed.
Page 255 Exercise 5 Answer
Given: y = 2x − 3
To find: Identify the slope and the y − intercept of the equation.
The equation is written in slope-intercept form.
y = 2x + (−3)
On comparing the equation by slope-intercept form we get,
The slope is 2 and the y-intercept is −3.
The slope is 2 and the y-intercept is −3.
Page 255 Exercise 6 Answer
Given: y = −0.5x + 2.5
To find: Identify the slope and the y−intercept of the equation.
The equation is written in slope-intercept form.
y = −0.5x + 2.5
On comparing the equation by slope-intercept form we get,
The slope is −0.5 and the y-intercept is 2.5.
The slope is −0.5 and the y-intercept is 2.5.
Page 255 Exercise 7 Answer
Given: y − 1 = −x
To find: Identify the slope and the y−intercept of the equation.
Write the equation in slope-intercept form:
y − 1 = −x
Move the constant to the right
y − 1 + 1 = −x + 1
Remove the opposites
y = −x + 1
On comparing the equation by slope-intercept form we get,
The slope is −1 and the y-intercept is 1.
The slope is −1 and the y−intercept is 1.
Page 255 Exercise 8 Answer
Given: \(y=\frac{2}{3} x-2\)
To find: Graph the equation.
From the slope-intercept form of a line, it follows:
m = \(\frac{2}{3}\), b = -2
Since the y-intercept of the line is −2, it follows that the line passes through the point (0,−2)
Draw the graph of the equation and plot point (0,−2),
The graph of the equation is shown below,
Page 255 Exercise 9 Answer
Given: y = −2x + 1
To find: Graph the equation.
From the slope-intercept form of a line, it follows:
m = −2,b = 1
Since the y-intercept of the line is 1, it follows that the line passes through the point (0,1).
Draw the graph of the equation and plot point (0,1),
The graph of the equation is shown below,
Page 255 Exercise 10 Answer
Given: y − x = 5
To find: Solve the equation for y.
y – x = 5
Move the variable to the right-hand side by adding its opposite to both sides,
y − x + x = 5 + x
Since two opposites add up to zero, remove them from the expression,
y = 5 + x
Use the commutative property to reorder the terms,
y = x + 5
Therefore, the value of y is x + 5.
Page 255 Exercise 11 Answer
Given: y + 0.2x = −4
To find: Solve the equation for y.
y + 0.2x = -4
Move the variable to the right-hand side by adding its opposite to both sides
y + 0.2x − 0.2x = −4−0.2x
Since two opposites add up to zero, remove them from the expression
y = −4−0.2x
Use the commutative property to reorder the terms,
y = −0.2x−4
Therefore, the value of y is −0.2x−4.
Page 255 Exercise 12 Answer
Given: \(-\frac{2}{3} x+y=8\)
To find: Solve the equation for y.
\(-\frac{2}{3} x+y=8\)Move the expression to the right-hand side by adding its opposite to both sides,
\(-\frac{2}{3} x+y+\frac{2}{3} x=8+\frac{2}{3} x\)Since two opposites add up to zero, remove them from the expression,
\(y=8+\frac{2}{3} x\)Use the commutative property to reorder the terms,
\(y=\frac{2}{3} x+8\)The value of y is \(\frac{2}{3} x+8\).