Question

Write an equation in slope-intercept form of the line that passes through (4,4)
and (5,−1)
.(1 point)
An equation is

Answer 1

To write the equation of the line in slope-intercept form \(y = mx + b\), we first need to find the slope \(m\) using the two points (4, 4) and (5, -1).

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

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

Substituting the given points:

\[
m = \frac{-1 - 4}{5 - 4} = \frac{-5}{1} = -5
\]

Now that we have the slope \(m = -5\), we can use one of the points to find \(b\), the y-intercept. We can use the point (4, 4):

\[
y = mx + b
\]

Substituting in the values for \(x\), \(y\), and \(m\):

\[
4 = -5(4) + b
\]

Calculating the right side:

\[
4 = -20 + b
\]

Solving for \(b\):

\[
b = 4 + 20 = 24
\]

Now we can write the equation of the line in slope-intercept form:

\[
y = -5x + 24
\]

So, the equation of the line that passes through the points (4, 4) and (5, -1) is:

\[
\boxed{y = -5x + 24}
\]