Question

Write the equation of the line in slope-intercept form that passes through the points (−4,−1)
, (3,−2)
.(1 point)
The equation in slope-intercept form is $$
.

Answer 1

To find the equation of the line in slope-intercept form (y = mx + b) that passes through the points (-4, -1) and (3, -2), we first need to calculate the slope (m) using the formula:

\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]

Using the points (-4, -1) as \((x_1, y_1)\) and (3, -2) as \((x_2, y_2)\):

\[
m = \frac{-2 - (-1)}{3 - (-4)} = \frac{-2 + 1}{3 + 4} = \frac{-1}{7}
\]

Now that we have the slope \(m = -\frac{1}{7}\), we can use one of the points (let's use (-4, -1)) to find the y-intercept (b). The equation of the line can be expressed as:

\[
y = mx + b
\]

Substituting the slope and the coordinates of the point (-4, -1):

\[
-1 = -\frac{1}{7}(-4) + b
\]

Calculating \(-\frac{1}{7}(-4)\):

\[
-1 = \frac{4}{7} + b
\]

Now, isolate \(b\):

\[
b = -1 - \frac{4}{7}
\]

Converting -1 to a fraction with a denominator of 7:

\[
b = -\frac{7}{7} - \frac{4}{7} = -\frac{11}{7}
\]

Now we have the slope \(m = -\frac{1}{7}\) and the y-intercept \(b = -\frac{11}{7}\). Therefore, the equation of the line in slope-intercept form is:

\[
y = -\frac{1}{7}x - \frac{11}{7}
\]

So the final answer is:

\[
\boxed{y = -\frac{1}{7}x - \frac{11}{7}}
\]