Question

0,2) (1, -1) 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) using the given points (0, 2) and (1, -1).

1. **Calculate the slope (m)**:
The formula for the slope between two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by:

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

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

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

2. **Use the slope to find the y-intercept (b)**:
We can use one of the points along with the slope to solve for b. We'll use the point \((0, 2)\):

The slope-intercept form is:

\[
y = mx + b
\]

Substituting the values we have:

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

\[
2 = b
\]

3. **Write the equation of the line**:
Now that we have both m and b, we can write the equation of the line:

\[
y = -3x + 2
\]

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

\[
y = -3x + 2
\]