What is the equation of the line that passes through the points (−3,4)

Question

and (−6,3)
? Write the answer in slope-intercept form.(1 point)
y=
(
)x+

Answer 1

To find the equation of the line that passes through the points $(-3,4)$ and $(-6,3)$, we need to determine the slope and then use the point-slope form of a line.

1. Calculate the slope (m):

The formula for the slope $m$ between two points $(x_1,y_1)$ and $(x_2,y_2)$ is:

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

Plugging in our points:

• $(x_1,y_1)=(-3,4)$
• $(x_2,y_2)=(-6,3)$

$$m=\frac{3-4}{-6-(-3)}=\frac{-1}{-6+3}=\frac{-1}{-3}=\frac{1}{3}$$

2. Use the point-slope form to find the equation:

The point-slope form of the equation of a line is given by:

$$y-y_1=m(x-x_1)$$

Using the slope $m=\frac{1}{3}$ and the point $(-3,4)$:

$$y-4=\frac{1}{3}(x+3)$$

3. Convert to slope-intercept form (y = mx + b):

First, distribute on the right side:

$$y-4=\frac{1}{3}x+1$$

Now, add 4 to both sides:

$$y=\frac{1}{3}x+1+4$$ $$y=\frac{1}{3}x+5$$

So, the equation of the line in slope-intercept form is:

$$\boxed{{\displaystyle y=\frac{1}{3}x+5}}$$