Answer
$y = -\frac{1}{8}x + 6$
Work Step by Step
The equation of the line given is in slope-intercept form, which is given by the formula $y = mx + b$, where $m$ is the slope.
Therefore, the slope of the given equation is $8$.
The line that we want to find would have to have a slope that is the negative reciprocal of the slope of the given line. Therefore, the slope of the line that we want to find is $-\frac{1}{8}$.
We can use this slope and the point given to plug into the formula for the point-slope form of an equation of a line, which is given by the following formula:
$y - y_1 = m(x - x_1)$, 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:
$y - 4.5 = -\frac{1}{8}(x - 12)$
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.
$y - 4.5 = -\frac{1}{8}x + \frac{12}{8}$
Simplify the fraction:
$y - 4.5 = -\frac{1}{8}x + 1.5$
Isolate $y$ by adding $4.5$ to both sides of the equation:
$y = -\frac{1}{8}x + 6$
