Question

write the slope intercept form of the equation of the line through the given point.
through: (-5,0) and (0,5)

Answer 1

To find the slope-intercept form (y = mx + b) of the line passing through the points \((-5, 0)\) and \((0, 5)\), we first need to determine the slope (m) of the line using the formula:

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

Using the points \((x_1, y_1) = (-5, 0)\) and \((x_2, y_2) = (0, 5)\):

\[
m = \frac{5 - 0}{0 - (-5)} = \frac{5}{5} = 1
\]

Now that we have the slope \(m = 1\), we can use one of the points to find the y-intercept (b). We can use the point \((0, 5)\):

Since the point \((0, 5)\) corresponds to the y-intercept, we have \(b = 5\).

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

\[
y = mx + b
\]

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

\[
y = 1x + 5
\]

or simply:

\[
y = x + 5
\]

This is the slope-intercept form of the equation of the line.