Question

Write the equation of the line in slope-intercept form that passes through the points (-4, -1) and (3, -2)

Answer 1

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

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

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

Substituting the given points (-4, -1) and (3, -2):

\[
(x_1, y_1) = (-4, -1) \quad \text{and} \quad (x_2, y_2) = (3, -2)
\]

Calculating the slope:

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

Now that we have the slope \( m = -\frac{1}{7} \), we can use one of the points to find the y-intercept \( b \). We can use the point (-4, -1). The slope-intercept form is:

\[
y = mx + b
\]

Substituting in the values we have:

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

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

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

To isolate \( b \), we subtract \( \frac{4}{7} \) from both sides:

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

Converting -1 into 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 \( b = -\frac{11}{7} \).

Putting it all together, the equation of the line in slope-intercept form is:

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