Question

points: (0,1) (1,-4)
Write the equation of the line in slope-intercept form.

(1 point)
Responses

y=−5x−1

y=5x+1

y=−5x+1

−5x−y=−1

Answer 1

To find the equation of the line in slope-intercept form \(y = mx + b\), we first need to determine the slope \(m\) using the two given points \((0,1)\) and \((1,-4)\).

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

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

Using the points \((0,1)\) as \((x_1,y_1)\) and \((1,-4)\) as \((x_2,y_2)\):

\[
m = \frac{-4 - 1}{1 - 0} = \frac{-5}{1} = -5
\]

Now we have the slope \(m = -5\).

Next, we can use one of the points to find \(b\), the y-intercept. We can use the point \((0,1)\):

Substituting \(x = 0\) and \(y = 1\) into the equation \(y = mx + b\):

\[
1 = -5(0) + b
\]
\[
1 = b
\]

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

\[
y = -5x + 1
\]

So the correct response is:

**y = −5x + 1**.