Use the image to answer the question.

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.

(1 point)
Responses

y=−5x−1
y equals negative 5 x minus 1

y=−5x+1
y equals negative 5 x plus 1

y=5x+1
y equals 5 x plus 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 points that lie on the line: \( (0, 1) \) and \( (1, -4) \).

1. Calculate the slope (m): The formula for slope \(m\) is given by:

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

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

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

2. Use one point to find the y-intercept (b): The point \( (0, 1) \) gives us the y-intercept directly, where \(x = 0\) and \(y = 1\). Thus, \(b = 1\).

3. Write the equation: Now we substitute the values of \(m\) and \(b\) into the slope-intercept form:

   \[ y = -5x + 1 \]

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

\[ y = -5x + 1 \]

The correct response is:

y = −5x + 1.