Question

Write the equation of the line in slope-intercept form.
(0,2) (1, -1)

Answer 1

To write the equation of the line in slope-intercept form (y = mx + b), we first need to determine the slope (m) of the line passing through the two points (0, 2) and (1, -1).

The formula for the slope (m) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is:

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

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

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

Now that we have the slope, we can use one of the points to find the y-intercept (b). Since the point (0, 2) is on the y-axis, the y-intercept is simply:

\[
b = 2
\]

Now we can write the equation of the line in slope-intercept form:

\[
y = mx + b
\]

Substituting the values of m and b we found:

\[
y = -3x + 2
\]

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

\[
\boxed{y = -3x + 2}
\]