Question

write the equation of the line in slope intercept form when the coordinates are
(1,-1) (0,2)

Answer 1

To find the equation of the line in slope-intercept form (y = mx + b) using the coordinates (1, -1) and (0, 2), we first need to determine the slope (m) of the line.

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

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

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

Now plug in the values:

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

Now that we have the slope (m = -3), we can use one of the points to find the y-intercept (b). Let's use the point (0, 2) where \(x = 0\) gives the y-intercept directly.

Thus, \(b = 2\).

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

\[
y = -3x + 2
\]

So the equation of the line is:

\[
y = -3x + 2
\]