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

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

(1 point)
y
=
x+

Answer 1

To find the equation of the line in slope-intercept form (\(y = mx + b\)), we first need to determine the slope (\(m\)) of the line and the y-intercept (\(b\)).

Step 1: Find the slope (\(m\)):

The slope of a line can be calculated using the formula:

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

Using the points \((0, 2)\) and \((1, -1)\):

• \( (x_1, y_1) = (0, 2) \)
• \( (x_2, y_2) = (1, -1) \)

Now substituting the coordinates into the slope formula:

\[ m = \frac{-1 - 2}{1 - 0} = \frac{-3}{1} = -3 \]

Step 2: Find the y-intercept (\(b\)):

We know the slope \(m = -3\) and we can use one of the points to find the y-intercept. Let’s use the point \((0, 2)\):

In the slope-intercept form, when \(x = 0\):

\[ y = mx + b \ 2 = -3(0) + b \ 2 = b \]

Step 3: Write the equation:

Now that we have \(m\) and \(b\), we can write the equation:

\[ y = -3x + 2 \]

Thus, the final answer in the required format is:

\[ y = -3x + 2 \]