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 2 right parenthesis and left parenthesis 1 comma negative 1 right parenthesis.

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

(1 point)
Remaining Attempts : 3
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Answer 1

To write the equation of a 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 formula is:
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]
Using the points \((0, 2)\) and \((1, -1)\):
- \(y_1 = 2\), \(y_2 = -1\)
- \(x_1 = 0\), \(x_2 = 1\)

Substitute these values:
\[
m = \frac{-1 - 2}{1 - 0} = \frac{-3}{1} = -3
\]

2. **Find the y-intercept \(b\)**:
The y-intercept \(b\) is the value of \(y\) when \(x = 0\). From the point \((0, 2)\), we can see:
\[
b = 2
\]

3. **Write the equation**:
Now, substitute the slope \(m\) and the y-intercept \(b\) into the slope-intercept form:
\[
y = -3x + 2
\]

Thus, the equation of the line in slope-intercept form is:
\[
\boxed{y = -3x + 2}
\]