Question

give the slope and the y-intercept of the line with the given equation. then, graph the linear equation.
y = 3x + 6
what is the slope? select the correct choice below and fill in any answer boxes within your choice.
a. the slope is \\(\square\\) (simplify your answer.)
b. the slope is undefined.
what is the y-intercept? select the correct choice below and fill in any answer boxes within your choice.
a. the y-intercept is \\(\square\\) (type an integer or a simplified fraction.)
b. there is no y-intercept.
graph the equation.
click to enlarge graph

Explanation:

Step1: Identify slope-intercept form

The line equation is in $y=mx+b$ form, where $m$ = slope, $b$ = y-intercept.
Given equation: $y=3x+6$

Step2: Extract the slope

Match $y=3x+6$ to $y=mx+b$: $m=3$

Step3: Extract the y-intercept

Match $y=3x+6$ to $y=mx+b$: $b=6$

Step4: Identify graph points

• Y-intercept point: $(0, 6)$
• Use slope $\frac{3}{1}$ to find a second point: from $(0,6)$, move 1 right, 3 up to $(1,9)$; or 1 left, 3 down to $(-1,3)$

Answer:

Slope:

A. The slope is $3$

Y-intercept:

A. The y-intercept is $6$

Graph Instructions:

Plot the points $(0, 6)$ and $(1, 9)$ (or $(-1, 3)$), then draw a straight line through them to represent $y=3x+6$.