Question

What is the of the line in slope- intercept from. (1,-1) (0,2)

Answer 1

To find the equation of the line in slope-intercept form (y = mx + b) using the points (1, -1) and (0, 2), we first need to calculate 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):
- \((x_1, y_1) = (1, -1)\)
- \((x_2, y_2) = (0, 2)\)

Substituting in the values:

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

Now that we have the slope \( m = -3 \), we will use one of the points to find the y-intercept \( b \). The point (0, 2) is particularly useful because it directly gives us the value of \( b \).

The equation can be written as:

\[
y = mx + b
\]

Substituting the values of \( m \) and \( b \):

\[
y = -3x + 2
\]

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

\[
y = -3x + 2
\]