﻿ Graph Linear Functions Worksheet - Page 13 | Problems & Solutions

# Graph Linear Functions Worksheet - Page 13

Graph Linear Functions Worksheet
• Page 13
121.
Find the slope and $y$-intercept of the function $f$($x$) = $\frac{4}{5}$$x$ + 7.
 a. Slope = -$\frac{4}{5}$, $y$-intercept = 9 b. Slope = $\frac{4}{5}$, $y$-intercept = 7 c. Slope = $\frac{5}{6,}$$y$-intercept = 7 d. None of the above

#### Solution:

f(x) = 45x + 7
[Original equation.]

f(x) = mx + c
[Standard equation.]

The slope of the function, m is 4 / 5 and the y-intercept, c is 7.
[Combine with the standard equation.]

122.
Find the slope and $y$-intercept of the function $f$($x$) = - 5($x$ - 2) + 2 .
 a. Slope = -4 and $y$-intercept is 11 b. Slope = -5 and $y$-intercept is 12 c. Slope = -6 and $y$-intercept is 13 d. None of the above

#### Solution:

f(x) = -5(x - 2) + 2
[Original function.]

f(x) = -5x + 10 + 2
[Multiply.]

f(x) = -5x + 12
[Multiply.]

f(x) = mx + c
[Standard function.]

The slope of the function, m is -5 and the y-intercept, c is 12.
[Compare the obtained equation with the standard equation.]

123.
Which of the following is not a linear function?
 a. $y$ = ($x$ + 5) + 2$x$ b. $y$ = $x$5 + 2 c. $y$ = $\frac{x}{5}$ + 2 d. None of the above

#### Solution:

A function in the form of f(x) = mx + c is called a linear function.
[In a linear function, the exponent of x must be 1.]

Among the choices the function y = x5 + 2 is not in the form of linear function.
[The exponent of x is 5.]

So, the function y = x5 + 2 is not a linear function.

124.
Which of the graphs best suits the equation $y$ = $x$ + 2 ?

 a. Graph 1 b. Graph 2 c. Graph 3 d. Graph 4

#### Solution:

y = - 23x + 2
[Original equation.]

y = - 23(0) + 2
[Substitute 0 for x.]

y = 2
[Simplify.]

y = - 23(1) + 2
[Substitute 1 for x.]

y = 43
[Simplify.]

y = - 23(2) + 2
[Substitute 2 for x.]

y = 23
[Simplify.]

y = - 23(3) + 2
[Substitute 3 for x.]

y = 0
[Simplify.]

Among the choices, graph 2 satisfies the condition.
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