Question

Using the graph, derive the equation of the line in slope-intercept form (-2,2) (0,1)

Answer 1

To find the equation of the line in slope-intercept form \(y = mx + b\), where \(m\) is the slope and \(b\) is the y-intercept, we can follow these steps:

1. **Calculate the slope (m)**:
The slope \(m\) is given by the formula:

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

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

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

2. **Substitute the slope and one of the points into the point-slope form to find b**:
We'll use the point \((0, 1)\), which is also the y-intercept.

Since the coordinates of this point are \(x = 0\) and \(y = 1\), we can directly see that \(b = 1\).

3. **Write the equation in slope-intercept form**:
Now that we have the slope and the y-intercept, we can write the equation of the line:

\[
y = -\frac{1}{2}x + 1
\]

Thus, the equation of the line in slope-intercept form is:

\[
y = -\frac{1}{2}x + 1
\]