Question

Derive the equation of the line in slope-intercept form. the numbers are (0,2) and (1,-1)

Answer 1

To derive the equation of the line in slope-intercept form (y = mx + b), we need to find the slope (m) and the y-intercept (b).

First, let's calculate the slope (m) using the two points given: (0, 2) and (1, -1).

The formula for the slope is:

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

Substituting the points into the formula:

- \( (x_1, y_1) = (0, 2) \)
- \( (x_2, y_2) = (1, -1) \)

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

Now we have the slope, \( m = -3 \).

Next, we can use one of the points to find the y-intercept (b). Since we are using the point (0, 2), we can substitute \( x = 0 \) and \( y = 2 \) into the slope-intercept form:

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

Now we have both the slope and the y-intercept:

- Slope (m) = -3
- Y-intercept (b) = 2

Putting it all together, the equation of the line in slope-intercept form is:

\[
y = -3x + 2
\]