Question

exercise 3
directions: choose the best answer from the four choices given. answers are on page 281.

1. if $f(x)=2x - 4$, then $f(-3) = $?

a. -10
b. -7
c. 2
d. 10

1. what is the slope of the line $y = 5x + 7$?

a. 7
b. 5
c. 2
d. $\frac{7}{5}$

1. what is the slope of a line that passes through $(0, -5)$ and $(8, 27)$?

a. 4
b. 2
c. $\frac{8}{32}$
d. $-\frac{8}{32}$

1. the points $(-3, 5)$ and $(8, 5)$ lie on a line in the $xy$-plane. what is the slope of the line?

a. -5
b. 0
c. 5
d. the slope is undefined

1. the figure below is the graph of which of the following equations?

(graph: a line with $y$-intercept $(0, 3)$ and $x$-intercept $(6, 0)$)
a. $x + 2y = 6$
b. $2x + y = 6$
c. $x + \frac{y}{2} = 6$
d. $\frac{x}{2} + y = 2$

Explanation:

Question 1

Step1: Substitute \( x = -3 \) into \( f(x) \)

Given \( f(x) = 2x - 4 \), substitute \( x = -3 \): \( f(-3) = 2(-3) - 4 \)

Step2: Calculate the value

\( 2(-3) = -6 \), so \( f(-3) = -6 - 4 = -10 \)

The equation of a line in slope - intercept form is \( y = mx + b \), where \( m \) is the slope and \( b \) is the y - intercept. For the line \( y = 5x+7 \), comparing with \( y = mx + b \), we can see that \( m = 5 \).

Step1: Recall the slope formula

The slope \( m \) of a line passing through two points \( (x_1,y_1) \) and \( (x_2,y_2) \) is given by \( m=\frac{y_2 - y_1}{x_2 - x_1} \)

Step2: Identify the points

Here, \( (x_1,y_1)=(0, - 5) \) and \( (x_2,y_2)=(8,27) \)

Step3: Substitute into the formula

\( m=\frac{27-(-5)}{8 - 0}=\frac{27 + 5}{8}=\frac{32}{8}=4 \)

Answer:

A. -10

Question 2