Answer:
The equation of required line is: ![\mathbf{5x-8y+34=0}](https://tex.z-dn.net/?f=%5Cmathbf%7B5x-8y%2B34%3D0%7D)
Step-by-step explanation:
We need to write equation in the form Ax+By+C=0 of the line parallel to
and through the point (-2,3)
First we need to find slope and y-intercept of the required line.
Using equation of line
to find slope.
Since the given line and required lines are parallel there slope is same.
Writing equation in slope intercept form:
where m is slope.
![5x-8y+12=0 \\-8y=-5x-12\\\frac{-8y}{-8y}=\frac{-5x}{-8}-\frac{12}{-8}\\y=\frac{5}{8}x+\frac{3}{4}](https://tex.z-dn.net/?f=5x-8y%2B12%3D0%20%5C%5C-8y%3D-5x-12%5C%5C%5Cfrac%7B-8y%7D%7B-8y%7D%3D%5Cfrac%7B-5x%7D%7B-8%7D-%5Cfrac%7B12%7D%7B-8%7D%5C%5Cy%3D%5Cfrac%7B5%7D%7B8%7Dx%2B%5Cfrac%7B3%7D%7B4%7D)
So, the slope m = 5/8
The slope of required line is ![m=\frac{5}{8}](https://tex.z-dn.net/?f=m%3D%5Cfrac%7B5%7D%7B8%7D)
Now finding y-intercept using slope
and point(-2,3)
![y=mx+b\\3=\frac{5}{8}(-2)+b\\3=\frac{-5}{4}+b\\b=3+\frac{5}{4}\\b=\frac{3*4+5}{4}\\b=\frac{12+5}{4}\\b=\frac{17}{4}](https://tex.z-dn.net/?f=y%3Dmx%2Bb%5C%5C3%3D%5Cfrac%7B5%7D%7B8%7D%28-2%29%2Bb%5C%5C3%3D%5Cfrac%7B-5%7D%7B4%7D%2Bb%5C%5Cb%3D3%2B%5Cfrac%7B5%7D%7B4%7D%5C%5Cb%3D%5Cfrac%7B3%2A4%2B5%7D%7B4%7D%5C%5Cb%3D%5Cfrac%7B12%2B5%7D%7B4%7D%5C%5Cb%3D%5Cfrac%7B17%7D%7B4%7D)
So, the equation of required line having slope
and y-intercept ![b=\frac{17}{4}](https://tex.z-dn.net/?f=b%3D%5Cfrac%7B17%7D%7B4%7D)
![y=mx+b\\y=\frac{5}{8}x+\frac{17}{4}\\y=\frac{5x+17*2}{8}\\y= \frac{5x+34}{8} \\8y=5x+34\\5x-8y+34=0](https://tex.z-dn.net/?f=y%3Dmx%2Bb%5C%5Cy%3D%5Cfrac%7B5%7D%7B8%7Dx%2B%5Cfrac%7B17%7D%7B4%7D%5C%5Cy%3D%5Cfrac%7B5x%2B17%2A2%7D%7B8%7D%5C%5Cy%3D%20%5Cfrac%7B5x%2B34%7D%7B8%7D%20%20%5C%5C8y%3D5x%2B34%5C%5C5x-8y%2B34%3D0)
So, The equation of required line is: ![\mathbf{5x-8y+34=0}](https://tex.z-dn.net/?f=%5Cmathbf%7B5x-8y%2B34%3D0%7D)