Question

quiz 8.3.3: patterns and lines
question 1
what is the equation of the following line? be sure to scroll down first to see all answer options.
a. $y = 21x$
b. $y = 7x$
c. $y = -7x$
d. $y = -3x$
e. $y = \frac{1}{5}x$
f. $y = 3x$

question 2
what is the equation of the following line? be sure to scroll down first to see all answer options.
a. $y = -\frac{1}{3}x$
b. $y = 3x$
c. $y = -3x$
d. $y = x$
e. $y = \frac{1}{3}x$
f. $y = -2x$

Explanation:

Question 1

Step1: Recall slope-intercept form

The line passes through the origin $(0,0)$, so its equation is $y=mx$, where $m$ is the slope.

Step2: Calculate the slope

Use the point $(3,21)$: $m=\frac{21}{3}=7$.

Step3: Match to options

The equation is $y=7x$.

Question 2

Step1: Recall slope-intercept form

The line passes through the origin $(0,0)$, so its equation is $y=mx$, where $m$ is the slope.

Step2: Calculate the slope

Use the point $(3,-9)$: $m=\frac{-9}{3}=-3$.

Step3: Match to options

The equation is $y=-3x$.

Answer:

1. B. $y = 7x$
2. C. $y = -3x$