Question

question 10 of 10
which of the following graphs represents the equation y = 3x + 2?

a
(1,6)
(0,3)

b
(2,8)
(0,2)

c
(2,8)
(-1,-1)

d
(1,0)
(0,-2)

a. graph a

b. graph b

c. graph c

d. graph d

Explanation:

Step1: Recall the slope - intercept form

The equation of a line in slope - intercept form is $y = mx + b$, where $m$ is the slope and $b$ is the y - intercept. For the equation $y=3x + 2$, the slope $m = 3$ and the y - intercept $b = 2$. This means the line should cross the y - axis at $(0,2)$ and have a positive slope (since $m = 3>0$, the line should be increasing from left to right).

Step2: Analyze each graph

• Graph A: The y - intercept is at $(0,6)$, not $(0,2)$, so it does not represent $y = 3x+2$.
• Graph B: The slope of the line appears to be negative (decreasing from left to right), but the slope of $y = 3x + 2$ is positive. So it does not represent $y=3x + 2$.
• Graph C: The y - intercept is at $(0,2)$, and we can check a point. Let's take $x=- 1$, then $y=3\times(-1)+2=-1$. The point $(-1,-1)$ lies on the line, and the slope is positive (increasing from left to right). So this graph represents $y = 3x+2$.
• Graph D: The y - intercept is at $(0,-2)$ and the slope is negative, so it does not represent $y = 3x + 2$.

Answer:

C. Graph C