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)

Answer 1

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

1. **Find the slope \( m \)**:
The slope \( m \) is given by the formula:
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]

Using the points \( (0, 2) \) and \( (1, -1) \):
- \( (x_1, y_1) = (0, 2) \)
- \( (x_2, y_2) = (1, -1) \)

Substituting the values into the slope formula:
\[
m = \frac{-1 - 2}{1 - 0} = \frac{-3}{1} = -3
\]

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 that when \( x = 0 \), \( y = 2 \). Therefore, \( b = 2 \).

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

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