Question

Write the equation of this line in slope-intercept form.
A=0,6
B=-2,0

Answer 1

To find the equation of the line in slope-intercept form (y = mx + b) that passes through the points A(0, 6) and B(-2, 0), we need to determine the slope (m) first.

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

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

Using the given points A(0, 6) and B(-2, 0):

Let \(A = (x_1, y_1) = (0, 6)\) and \(B = (x_2, y_2) = (-2, 0)\).

Now, substitute the coordinates into the slope formula:

\[
m = \frac{0 - 6}{-2 - 0} = \frac{-6}{-2} = 3
\]

Now that we have the slope \(m = 3\), we can use point-slope form to find the equation of the line. We can use point A (0, 6) for this:

The point-slope form is:

\[
y - y_1 = m(x - x_1)
\]

Substituting \(m = 3\) and the coordinates of point A (0, 6):

\[
y - 6 = 3(x - 0)
\]

Simplifying this:

\[
y - 6 = 3x
\]

\[
y = 3x + 6
\]

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

\[
y = 3x + 6
\]