What is the equation in slope-intercept form of the line that passes through the points (-26, -11) and (39, 34)?

Steps to Solve

1. Calculate the Slope of the Line

To find the slope $m$ between two points $(x_1, y_1)$ and $(x_2, y_2)$, use the formula:

$$ m = \frac{y_2 - y_1}{x_2 - x_1} $$

For the points $(-26, -11)$ and $(39, 34)$, substitute:

$$ m = \frac{34 - (-11)}{39 - (-26)} = \frac{34 + 11}{39 + 26} = \frac{45}{65} = \frac{9}{13} $$

2. Use One of the Points to Find the Y-Intercept

Using the slope $m = \frac{9}{13}$ and one of the points, say $(39, 34)$, we can use the equation of a line in slope-intercept form:

$$ y = mx + b $$

Substituting the point into the equation:

$$ 34 = \frac{9}{13} \cdot 39 + b $$

3. Solve for the Y-Intercept, ( b )

Calculate the right side:

$$ 34 = \frac{351}{13} + b $$

Then, isolate ( b ):

$$ b = 34 - \frac{351}{13} $$

Convert ( 34 ) to have a common denominator:

$$ b = \frac{442}{13} - \frac{351}{13} = \frac{91}{13} $$

4. Write the Equation in Slope-Intercept Form

Now that we have the slope ( m ) and ( b ):

$$ y = \frac{9}{13} x + \frac{91}{13} $$

Since this does not match any answer choices directly, let's convert the ( b ) to proper form.

5. Identify the Equation for Final Review

The slope-intercept equation of the line that passes through both points can be arranged as follows:

$$ y = \frac{9}{13} x + 7 $$

as ( \frac{91}{13} ) simplifies to ( 7 ).