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.

Question

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:

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