Question

Use the image to answer the question.

A coordinate plane of 4 quadrants shows x and y axes ranging from negative 3 to 3 in increments of 1. A line with arrows at each end intercepts two plotted points, A and B. Point A is plotted at left parenthesis 0 comma negative 1 right parenthesis. Point B is plotted at left parenthesis 1 comma 1 right parenthesis. The coordinates are not labeled.

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

Answer 1

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

1. **Find the slope (m) between points A (0, -1) and B (1, 1)**:
The formula for slope is:
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]
Here, (x1, y1) = (0, -1) and (x2, y2) = (1, 1):
\[
m = \frac{1 - (-1)}{1 - 0} = \frac{1 + 1}{1} = \frac{2}{1} = 2
\]

2. **Find the y-intercept (b)**:
We can use one of the points to find b. We'll use point A (0, -1):
\[
y = mx + b
\]
Substituting \(x = 0\) and \(y = -1\):
\[
-1 = 2(0) + b \implies -1 = b
\]

3. **Write the equation in slope-intercept form**:
Now we have both the slope (m = 2) and the y-intercept (b = -1). The equation of the line is:
\[
y = 2x - 1
\]

Thus, the equation of the line in slope-intercept form is:
\[
y = 2x - 1
\]