Question

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

Answer 1

The equation in slope-intercept form of the line passing through the given points is: C. $y = \frac{9}{13}x + 7$

Given the following points:

• Points on the x-axis = (-26, 39)

• Points on the y-axis = (-11, 34)

To find the equation in slope-intercept form of the line passing through the given points:

Mathematically, the equation of slope is calculated by using this:

$Slope. \;m = \frac{Change \; in \; y \;axis}{Change \; in \; x \;axis} \\\\Slope. \;m = \frac{y_2 - y_1}{x_2 - x_1}$

Substituting the given points, we have:

$Slope. \;m = \frac{34 - [-11]}{39 - (-26)}\\\\Slope. \;m = \frac{34\; + \;11}{39 \;+ \; 26}\\\\Slope. \;m = \frac{45}{65}\\\\Slope. \;m = \frac{9}{13}$

The standard form of an equation of line is given by the formula;

$y = mx + b$

Where:

• x and y are the points.

• m is the slope.

• b is the intercept.

We would find the intercept:

$-11 = \frac{9}{13}(-26) + b\\\\ -11 = -18 + b\\\\b = -11 + 18$

Intercept, b = 7

The equation in slope-intercept form of the line is:

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

Read more: brainly.com/question/18123312