The equation of required line is: ![y=\frac{-1}{4}x+\frac{5}{4}](https://tex.z-dn.net/?f=y%3D%5Cfrac%7B-1%7D%7B4%7Dx%2B%5Cfrac%7B5%7D%7B4%7D)
Step-by-step explanation:
We are given point (1,1) and a line having equation y=4x+6
We need to find a line perpendicular to the given line.
The standard form of slope-intercept is: y=mx+b
where m is slope and b is y-intercept.
So, comparing the given equation with standard line we get,
m= 4
Since the new line is perpendicular to the given line, so its slope will be -1/slope
So, slope of new line is m= -1/4
Now, finding y-intercept
Using the given point and slope we get:
![y=mx+b\\1=\frac{-1}{4}(1)+b\\1=\frac{-1}{4}+b\\b=1+\frac{1}{4}\\b=\frac{4+1}{4}\\b=\frac{5}{4}](https://tex.z-dn.net/?f=y%3Dmx%2Bb%5C%5C1%3D%5Cfrac%7B-1%7D%7B4%7D%281%29%2Bb%5C%5C1%3D%5Cfrac%7B-1%7D%7B4%7D%2Bb%5C%5Cb%3D1%2B%5Cfrac%7B1%7D%7B4%7D%5C%5Cb%3D%5Cfrac%7B4%2B1%7D%7B4%7D%5C%5Cb%3D%5Cfrac%7B5%7D%7B4%7D)
So, y-intercept is ![b=\frac{5}{4}](https://tex.z-dn.net/?f=b%3D%5Cfrac%7B5%7D%7B4%7D)
The equation of new line having slope -1/4 and y-intercept = 5/4 is:
![y=mx+b\\y=\frac{-1}{4}x+\frac{5}{4}](https://tex.z-dn.net/?f=y%3Dmx%2Bb%5C%5Cy%3D%5Cfrac%7B-1%7D%7B4%7Dx%2B%5Cfrac%7B5%7D%7B4%7D)
So, the equation of required line is: ![y=\frac{-1}{4}x+\frac{5}{4}](https://tex.z-dn.net/?f=y%3D%5Cfrac%7B-1%7D%7B4%7Dx%2B%5Cfrac%7B5%7D%7B4%7D)
Keywords: Slope-intercept form is:
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