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 $$
.

1 answer

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:

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