Answer:
The equation in slope-intercept form of the line that passes through the point (12, 5) and is perpendicular to the line is:
- [tex]y=-\frac{1}{34}x+\frac{91}{17}[/tex]
Step-by-step explanation:
We know the slope-intercept form of the line equation
[tex]y=mx+b[/tex]
where m is the slope and b is the y-intercept
Given the line
[tex]y=34x-8[/tex]
comparing with the slope-intercept form of the line equation
The slope m = 34
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 = 34
Thus, the slope of the the new perpendicular line = – 1/m = -1/34 = -1/34
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 slope = -1/35 and the point (12, 5)
[tex]y-y_1=m\left(x-x_1\right)[/tex]
[tex]y-5=-\frac{1}{34}\left(x-12\right)[/tex]
Add 5 to both sides
[tex]y-5+5=-\frac{1}{34}\left(x-12\right)+5[/tex]
[tex]y=-\frac{1}{34}x+\frac{91}{17}[/tex]
Therefore, the equation in slope-intercept form of the line that passes through the point (12, 5) and is perpendicular to the line is:
- [tex]y=-\frac{1}{34}x+\frac{91}{17}[/tex]
