Question

Use the image to answer the 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

−5x−y=−1
negative 5 x minus y equals negative 1

y=−5x+1
y equals negative 5 x plus 1

y=5x+1
y equals 5 x plus 1

y=−5x−1
y equals negative 5 x minus 1
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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 given: (0, 1) and (1, -4).

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

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

Substituting the points (0, 1) and (1, -4):

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

Now that we have the slope \(m = -5\), we can use one of the points to find the y-intercept \(b\). We'll use the point (0, 1), where \(x = 0\) and \(y = 1\).

Using the slope-intercept form \(y = mx + b\):

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

Therefore, the equation of the line is:

\[
y = -5x + 1
\]

The correct response is:

**y = −5x + 1**.