Answer:
We conclude that the equation in slope-intercept form of the line that passes through (12,9) and is perpendicular to the graph of y = -3/4x + 1 will be:
Step-by-step explanation:
We know the slope-intercept form of the line equation
y = mx+b
where
Given the line
y = -3/4x + 1
comparing with the slope-intercept form of the line equation
The slope = m = -3/4
We know that a line perpendicular to another line contains a slope that is the negative reciprocal of the slope of the other line, such as:
slope = m = -3/4
Thus, the slope of the new perpendicular line = – 1/(-3/4) = 4/3
Using the point-slope form
[tex]y-y_1=m\left(x-x_1\right)[/tex]
where m is the slope of the line and (x₁, y₁) is the point
substituting the values of the slope = 4/3 and the point (12, 9)
[tex]y-y_1=m\left(x-x_1\right)[/tex]
[tex]y-9=\frac{4}{3}\left(x-12\right)[/tex]
Add 9 to both sides
[tex]y-9+9=\frac{4}{3}\left(x-12\right)+9[/tex]
[tex]y=\frac{4}{3}x-16+9[/tex]
[tex]y=\frac{4}{3}x-7[/tex]
Therefore, we conclude that the equation in slope-intercept form of the line that passes through (12,9) and is perpendicular to the graph of y = -3/4x + 1 will be:
