Question

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Graphing Equations Quick Check
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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

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

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

y=−5x−1
y equals negative 5 x minus 1

y=−5x+1

Answer 1

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

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

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

Substitute \((x_1, y_1) = (0, 1)\) and \((x_2, y_2) = (1, -4)\):

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

2. **Use the slope-intercept form**:
Now we know the slope \(m = -5\). Next, we need to find the y-intercept (b). When \(x = 0\), \(y\) is 1 (the y-coordinate of the point (0, 1)), so:

\[
b = 1
\]

3. **Write the equation in slope-intercept form**:
Now we can write the equation of the line:

\[
y = -5x + 1
\]

So, the correct response that matches this equation from the provided options is:

**y = -5x + 1**