Question

1. for which values of m would the system $y=2x+3$ and $y=mx-1$ have no solution?

a. $m=3$
b. $m=-2$
c. $m=1$
d. $m=2$

1. what is the y-intercept of the equation $y=-4x+8$?

a. 4
b. 0
c. -4
d. 8

Explanation:

Step1: Identify parallel line condition

A system of linear equations $y=a_1x+b_1$ and $y=a_2x+b_2$ has no solution if $a_1=a_2$ and $b_1
eq b_2$.

Step2: Match slopes for first problem

For $y=2x+3$ and $y=mx-1$, set $m=2$. Here $3
eq -1$, so no solution.

Step3: Recall slope-intercept form

The slope-intercept form is $y=mx+b$, where $b$ is the y-intercept.

Step4: Find y-intercept for second problem

For $y=-4x+8$, $b=8$, so the y-intercept is 8.

Answer:

1. d. $m=2$
2. d. 8