Question

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

​x−

​.

Answer 1

To find the equation of the line in slope-intercept form (\(y = mx + b\)), we'll start by calculating the slope (\(m\)) using the two points given: \((-4, -1)\) and \( (3, -2)\).

The slope formula is:

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

Here, \((x_1, y_1) = (-4, -1)\) and \((x_2, y_2) = (3, -2)\).

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'll use the point \((3, -2)\).

Using the slope-intercept form:

\[
y = mx + b
\]

Substituting \(m\) and the point \((3, -2)\):

\[
-2 = -\frac{1}{7} \cdot 3 + b
\]

Calculating:

\[
-2 = -\frac{3}{7} + b
\]

Now, isolate \(b\):

\[
b = -2 + \frac{3}{7}
\]

To combine, convert \(-2\) to a fraction with a denominator of 7:

\[
b = -\frac{14}{7} + \frac{3}{7} = -\frac{14 - 3}{7} = -\frac{11}{7}
\]

Now we have \(m\) and \(b\). The equation of the line in slope-intercept form is:

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

To rewrite this without the fraction in front of \(x\), we can multiply through by \(7\):

\[
7y = -x - 11
\]

Thus, the slope-intercept form remains:

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

However, since you were looking for it in the form of \(y = -x - \) something, it seems to be:

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

So, according to your question, you can replace the "something" with \(-\frac{11}{7}\):

The equation in slope-intercept form is \(y = -\frac{1}{7}x - \frac{11}{7}\).