Answer
$y = \frac{9}{2}x - 10$
Work Step by Step
First, we want to find the slope of the line. Since we are given two points on the line, we can use these to plug into the formula for slope.
The slope of a line is given by the following formula:
$m = \frac{y_2 - y_1}{x_2 - x_1}$
Let's plug in our points into this formula:
$m = \frac{35 - 8}{10 - 4}$
Subtract to simplify:
$m = \frac{27}{6}$
Simplify the fraction:
$m = \frac{9}{2}$
Now we can use the point-slope formula to find the equation of the line we want. The point-slope formula is given as:
$y - y_1 = m(x - x_1)$, where $(x_1, y_1)$ is a point on the line and $m$ is the slope of the line.
Let's plug in the points into the formula:
$y - 8 = \frac{9}{2}(x - 4)$
We are asked to write the equation in slope-intercept form, which is given by the following formula:
$y = mx + b$, where $m$ is the slope and $b$ is the y-intercept.
Use the distributive property:
$y - 8 = \frac{9}{2}x - \frac{36}{2}$
Simplify the fraction:
$y - 8 = \frac{9}{2}x - 18$
Isolate $y$ by adding $8$ to both sides of the equation:
$y = \frac{9}{2}x - 10$
