Question

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

question 6
what is the equation of the following line? be sure to scroll down first to see all answer options.
a. $y = -\frac{2}{3}x$
b. $y = \frac{3}{2}x$
c. $y = \frac{2}{3}x$
d. $y = 2x$
e. $y = 3x$
f. $y = -\frac{3}{2}x$

Explanation:

Question 5

Step1: Identify line form

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

Step2: Calculate slope $m$

Use points $(0,0)$ and $(-3,1)$:
$m=\frac{y_2-y_1}{x_2-x_1}=\frac{1-0}{-3-0}=-\frac{1}{3}$

Step3: Match to option

The equation is $y=-\frac{1}{3}x$, which is option E.

Question 6

Step1: Identify line form

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

Step2: Calculate slope $m$

Use points $(0,0)$ and $(-2,-3)$:
$m=\frac{y_2-y_1}{x_2-x_1}=\frac{-3-0}{-2-0}=\frac{3}{2}$

Step3: Match to option

The equation is $y=\frac{3}{2}x$, which is option B.

Answer:

Question 5: E. $y = -\frac{1}{3}x$
Question 6: B. $y = \frac{3}{2}x$