Question

passes through the given coordinates
4.
(29, 11) and (-3, -7)

Explanation:

Identify the given points

Find the coordinates of the two points from the image.
The first point is \( (9, 11) \) and the second point is \( (-3, -7) \).

Calculate the slope

Use the slope formula to find the slope \( m \) of the line.

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

Substitute the coordinates:

$$ m = \frac{-7 - 11}{-3 - 9} = \frac{-18}{-12} = \frac{3}{2} $$

Write the equation in point-slope form

Use the point-slope formula with the point \( (9, 11) \).

$$ y - y_1 = m(x - x_1) $$

Substitute \( m = \frac{3}{2} \) and the point \( (9, 11) \):

$$ y - 11 = \frac{3}{2}(x - 9) $$

Convert to slope-intercept form

Simplify the equation to the standard slope-intercept form \( y = mx + b \).

$$ y - 11 = \frac{3}{2}x - \frac{27}{2} $$

Add \( 11 \) (which is \( \frac{22}{2} \)) to both sides:

$$ y = \frac{3}{2}x - \frac{27}{2} + \frac{22}{2} $$

$$ y = \frac{3}{2}x - \frac{5}{2} $$

Answer:

\(y = \frac{3}{2}x - \frac{5}{2}\)