Question

practice 20
2/9/2026

1. match each equation with the slope and y-intercept of the line it represents.

equation slope and y-intercept
$y=-3x+\frac{1}{2}$ slope $-3$ and y-intercept $\frac{1}{2}$
$y=\frac{1}{2}x-3$ slope 0 and y-intercept 1
$y=x$ slope $\frac{1}{2}$ and y-intercept $-3$
$y=1$ slope 1 and y-intercept 0

for problems 2-5, graph the equation.

1. $y=\frac{1}{2}x-2$
2. $y=3x+2$

Explanation:

Step1: Identify slope-intercept form

The slope-intercept form of a line is $y=mx+b$, where $m$ is slope, $b$ is y-intercept.

Step2: Match first equation

For $y=-3x+\frac{1}{2}$, $m=-3$, $b=\frac{1}{2}$.
Matches: Slope $-3$ and y-intercept $\frac{1}{2}$

Step3: Match second equation

For $y=\frac{1}{2}x-3$, $m=\frac{1}{2}$, $b=-3$.
Matches: Slope $\frac{1}{2}$ and y-intercept $-3$

Step4: Match third equation

For $y=x$, rewrite as $y=1x+0$, so $m=1$, $b=0$.
Matches: Slope $1$ and y-intercept $0$

Step5: Match fourth equation

For $y=1$, rewrite as $y=0x+1$, so $m=0$, $b=1$.
Matches: Slope $0$ and y-intercept $1$

Step6: Verify graph for $y=\frac{1}{2}x-2$

1. y-intercept is $-2$ (point $(0,-2)$).
2. Slope $\frac{1}{2}$: move 2 right, 1 up from $(0,-2)$ to $(2,-1)$, repeat to $(4,0)$, $(6,1)$, $(8,2)$; plot and connect.

Step7: Verify graph for $y=3x+2$

1. y-intercept is $2$ (point $(0,2)$).
2. Slope $3$: move 1 right, 3 up from $(0,2)$ to $(1,5)$, $(2,8)$; move 1 left, 3 down to $(-1,-1)$, $(-2,-4)$; plot and connect.

Answer:

Matching Results:

• $y=-3x+\frac{1}{2}$ → Slope $-3$ and y-intercept $\frac{1}{2}$
• $y=\frac{1}{2}x-3$ → Slope $\frac{1}{2}$ and y-intercept $-3$
• $y=x$ → Slope $1$ and y-intercept $0$
• $y=1$ → Slope $0$ and y-intercept $1$

Graph Confirmations:

1. For $y=\frac{1}{2}x-2$: The provided graph is correct, passing through $(0,-2)$, $(2,-1)$, $(4,0)$, etc.
2. For $y=3x+2$: The provided graph is correct, passing through $(0,2)$, $(1,5)$, $(-1,-1)$, etc.