Answer:
The equation of line that passes through the point (8,-7) and is parallel to the line 5x+4y=16 is ![\mathbf{y=-\frac{5}{4}x+3}](https://tex.z-dn.net/?f=%5Cmathbf%7By%3D-%5Cfrac%7B5%7D%7B4%7Dx%2B3%7D)
Step-by-step explanation:
We need to write an equation of the line that passes through the point (8,-7) and is parallel to the line 5x+4y=16.
The equation will be of form
where m is slope and b is y-intercept.
Finding slope of the line:
Since both the lines are parallel, and we know that parallel lines have same slope.
The slope of given line
can be found by writing in slope-intercept form ![y=mx+b](https://tex.z-dn.net/?f=y%3Dmx%2Bb)
![5x+4y=16\\4y=-5x+16\\y=-\frac{5}{4}x+16](https://tex.z-dn.net/?f=5x%2B4y%3D16%5C%5C4y%3D-5x%2B16%5C%5Cy%3D-%5Cfrac%7B5%7D%7B4%7Dx%2B16)
Comparing with
the slope m is: ![m=-\frac{5}{4}](https://tex.z-dn.net/?f=m%3D-%5Cfrac%7B5%7D%7B4%7D)
So, the slope of required line is: ![m=-\frac{5}{4}](https://tex.z-dn.net/?f=m%3D-%5Cfrac%7B5%7D%7B4%7D)
Now, finding y-intercept b
y-intercept can be found using slope
and point (8,-7)
![y=mx+b\\-7=-\frac{5}{4}(8)+b\\-7=-5(2)+b\\-7=-10+b\\b=-7+10\\b=3](https://tex.z-dn.net/?f=y%3Dmx%2Bb%5C%5C-7%3D-%5Cfrac%7B5%7D%7B4%7D%288%29%2Bb%5C%5C-7%3D-5%282%29%2Bb%5C%5C-7%3D-10%2Bb%5C%5Cb%3D-7%2B10%5C%5Cb%3D3)
So, we get y-intercept: b=3
Now, the equation of required line having slope
and y-intercept b=3 is:
![y=mx+b\\y=-\frac{5}{4}x+3](https://tex.z-dn.net/?f=y%3Dmx%2Bb%5C%5Cy%3D-%5Cfrac%7B5%7D%7B4%7Dx%2B3)
So, the equation of line that passes through the point (8,-7) and is parallel to the line 5x+4y=16 ![\mathbf{y=-\frac{5}{4}x+3}](https://tex.z-dn.net/?f=%5Cmathbf%7By%3D-%5Cfrac%7B5%7D%7B4%7Dx%2B3%7D)