Answer:
Equation of line u in slope-intercept form is: ![\mathbf{y=\frac{1}{2}x+9 }](https://tex.z-dn.net/?f=%5Cmathbf%7By%3D%5Cfrac%7B1%7D%7B2%7Dx%2B9%20%7D)
Step-by-step explanation:
Equation of line t : y = -2x + 9.
We need to find equation of line u, which is perpendicular to line t and passes through point (-10,4)
The equation must be in slope-intercept form.
The general equation of slope-intercept form is:
where m is slope and b is y-intercept
Finding Slope:
If two lines are perpendicular, their slopes are opposite i.e ![m=-\frac{1}{m}](https://tex.z-dn.net/?f=m%3D-%5Cfrac%7B1%7D%7Bm%7D)
Slope of line t: y=-2x+9 we get m =-2 (Comparing with general form y=mx+b, we get m =-2)
Slope of line u: ![\frac{1}{2}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B2%7D)
So, we get Slope of line u: m= ![\frac{1}{2}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B2%7D)
Finding y-intercept:
Using slope m=
and point(-10,4) we can find y-intercept
![y=mx+b\\4=\frac{1}{2}(-10)+b\\4=-5+b\\b=4+5\\b=9](https://tex.z-dn.net/?f=y%3Dmx%2Bb%5C%5C4%3D%5Cfrac%7B1%7D%7B2%7D%28-10%29%2Bb%5C%5C4%3D-5%2Bb%5C%5Cb%3D4%2B5%5C%5Cb%3D9)
Equation of line u:
So, equation of line u, having slope m=
and y-intercept b=9, we get:
![y=mx+b\\y=\frac{1}{2}x+9](https://tex.z-dn.net/?f=y%3Dmx%2Bb%5C%5Cy%3D%5Cfrac%7B1%7D%7B2%7Dx%2B9)
So, Equation of line u in slope-intercept form is: ![\mathbf{y=\frac{1}{2}x+9 }](https://tex.z-dn.net/?f=%5Cmathbf%7By%3D%5Cfrac%7B1%7D%7B2%7Dx%2B9%20%7D)