Question

points are 5,-5 and 1, 5

Write an equation in slope-intercept form of the graph:

Answer 1

To find the equation in slope-intercept form \(y = mx + b\) using the points (5, -5) and (1, 5), we'll follow these steps:

1. **Calculate the slope (m)** using the formula:

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

Using the points (5, -5) as \((x_1, y_1)\) and (1, 5) as \((x_2, y_2)\):

\[
m = \frac{5 - (-5)}{1 - 5} = \frac{5 + 5}{1 - 5} = \frac{10}{-4} = -\frac{5}{2}
\]

2. **Use one of the points to find the y-intercept (b)**. We can use the point (5, -5) and the slope we just calculated:

\[
y = mx + b \implies -5 = -\frac{5}{2}(5) + b
\]
\[
-5 = -\frac{25}{2} + b
\]
\[
b = -5 + \frac{25}{2}
\]
\[
b = -\frac{10}{2} + \frac{25}{2} = \frac{15}{2}
\]

3. **Write the equation in slope-intercept form**:

Now that we have both the slope \(m = -\frac{5}{2}\) and the y-intercept \(b = \frac{15}{2}\), we can write the equation:

\[
y = -\frac{5}{2}x + \frac{15}{2}
\]

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