the equation of a line perpendicular to
and passes through the point (-6,8) is ![y=-4x+30](https://tex.z-dn.net/?f=y%3D-4x%2B30)
Step-by-step explanation:
We need to write equation of line perpendicular to
and passes through the point (-6,8)
Since the line
is in slope-inetercept form ![y=mx+b](https://tex.z-dn.net/?f=y%3Dmx%2Bb)
the slope of line m = 0.25
As, the new line is perpendicular to the given line so, slopes of lines that are perpendicular are: slope = -1/slope1
So, slope will be -1/0.25 = -4
Now, finding y-intercept.
![y=mx+b8=4(-6)+b\\8=-24+b\\b=8+24\\b=30](https://tex.z-dn.net/?f=y%3Dmx%2Bb8%3D4%28-6%29%2Bb%5C%5C8%3D-24%2Bb%5C%5Cb%3D8%2B24%5C%5Cb%3D30)
So, value of y-intercept b = 30
Now the equation of the required line having slope m= -4 and b =30 will be:
![y=mx+b\\y=-4x+30](https://tex.z-dn.net/?f=y%3Dmx%2Bb%5C%5Cy%3D-4x%2B30)
So, the equation of a line perpendicular to
and passes through the point (-6,8) is ![y=-4x+30](https://tex.z-dn.net/?f=y%3D-4x%2B30)
Keywords: Equation of line, slope-intercept form
Learn more about slope-intercept form at:
#learnwithBrainly