A line contains the points (-3, 2) and (0, 2). What is the equation of this line in slope-intercept form?

Question

A. y = 3x + 2
B. y = –3x + 2
C. y = –3
D. y = 2

Answer 1

To find the equation of the line that passes through the points $(-3,2)$ and $(0,2)$, we first need to determine the slope $m$. The formula for the slope between two points $(x_1,y_1)$ and $(x_2,y_2)$ is:

$$m=\frac{y_2-y_1}{x_2-x_1}$$

Using the given points $(-3,2)$ and $(0,2)$:

$$m=\frac{2-2}{0-(-3)}=\frac{0}{3}=0$$

The slope $m$ is 0, which means the line is horizontal.

In slope-intercept form ($y=mx+b$), since the slope $m$ is 0, the equation simplifies to:

$$y=0\cdot x+b$$
$$y=b$$

To find $b$, we use one of the given points. Plugging in the point $(0,2)$:

$$2=b$$

Thus, the equation of the line is:

$$y=2$$

So, the answer is:

$$\boxed{{\displaystyle D.y=2}}$$