Question

spiral review

1. label each line on the graph with its corresponding equation.

• line a: $y=2x + 3$
• line b: $y=-2x + 3$
• line c: $y=2x - 3$
• line d: $y=-2x - 3$

Explanation:

Step1: Identify slope and y-intercept

Use slope-intercept form $y=mx+b$, where $m$ is slope, $b$ is y-intercept.

Step2: Match positive slope lines

Lines with $m=2$ (upward slope):

• $y=2x+3$: $b=3$ (crosses $y$-axis at $(0,3)$)
• $y=2x-3$: $b=-3$ (crosses $y$-axis at $(0,-3)$)

Step3: Match negative slope lines

Lines with $m=-2$ (downward slope):

• $y=-2x+3$: $b=3$ (crosses $y$-axis at $(0,3)$)
• $y=-2x-3$: $b=-3$ (crosses $y$-axis at $(0,-3)$)

Step4: Assign to graph lines

• Upward line through $(0,3)$: $y=2x+3$ (Line $a$)
• Downward line through $(0,3)$: $y=-2x+3$ (Line $b$)
• Upward line through $(0,-3)$: $y=2x-3$ (Line $c$)
• Downward line through $(0,-3)$: $y=-2x-3$ (Line $d$)

Answer:

• The line with positive slope crossing the y-axis at $(0,3)$ is $\boldsymbol{y=2x+3}$ (Line $a$)
• The line with negative slope crossing the y-axis at $(0,3)$ is $\boldsymbol{y=-2x+3}$ (Line $b$)
• The line with positive slope crossing the y-axis at $(0,-3)$ is $\boldsymbol{y=2x-3}$ (Line $c$)
• The line with negative slope crossing the y-axis at $(0,-3)$ is $\boldsymbol{y=-2x-3}$ (Line $d$)