Question

An illustration of a coordinate plane with four quadrants shows the x-axis ranging from negative 9 to 9 and the y-axis ranging from negative 11 to 11 in increments of 1. A solid downward line with arrows at both ends is plotted on the graph. The line passes through the plotted points left parenthesis 0 comma 1 right parenthesis and left parenthesis 1 comma negative 4 right parenthesis.

Write the equation of the line in slope-intercept form.

Answer 1

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

1. **Find the slope (\(m\))**: The slope is calculated using the formula:

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

Using the points \((0, 1)\) and \((1, -4)\):

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

2. **Use the slope to find the y-intercept (\(b\))**: The line can be written using one of the points. We'll use the point \((0, 1)\):

\[
y = mx + b
\]

Substituting the slope and the point into the equation:

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

Thus,

\[
b = 1
\]

3. **Write the equation of the line**: Now we can put the slope and the y-intercept together:

\[
y = -5x + 1
\]

So, the equation of the line in slope-intercept form is:

\[
\boxed{y = -5x + 1}
\]