Answer:
The equation of the line in the form Ax+By=C is ![\mathbf{ x+4y=-7}](https://tex.z-dn.net/?f=%5Cmathbf%7B%20x%2B4y%3D-7%7D)
Step-by-step explanation:
We need to write an equation of line that have slope m= -1/4 and point(-7,0)
We would use slope-intercept form: ![y=mx+b](https://tex.z-dn.net/?f=y%3Dmx%2Bb)
where m is slope and b is y-intercept.
We are given slope m = -1/4 but we need to find y-intercept
Finding y-intercept
Using the slope m= -1/4 and point(-7,0) we can find y-intercept (b)
![y=mx+b\\0=-\frac{1}{4}(-7)+b\\0= \frac{7}{4}+b\\b=-\frac{7}{4}](https://tex.z-dn.net/?f=y%3Dmx%2Bb%5C%5C0%3D-%5Cfrac%7B1%7D%7B4%7D%28-7%29%2Bb%5C%5C0%3D%20%5Cfrac%7B7%7D%7B4%7D%2Bb%5C%5Cb%3D-%5Cfrac%7B7%7D%7B4%7D)
Now finding the equation of line having slope m= -1/4 and y-intercept b= -7/4
![y=mx+b\\y=-\frac{1}{4}x-\frac{7}{4}](https://tex.z-dn.net/?f=y%3Dmx%2Bb%5C%5Cy%3D-%5Cfrac%7B1%7D%7B4%7Dx-%5Cfrac%7B7%7D%7B4%7D)
Now converting into form Ax+By=C :
![y=-\frac{1}{4}x-\frac{7}{4}\\y=\frac{-x-7}{4}\\4y=-x-7\\x+4y=-7](https://tex.z-dn.net/?f=y%3D-%5Cfrac%7B1%7D%7B4%7Dx-%5Cfrac%7B7%7D%7B4%7D%5C%5Cy%3D%5Cfrac%7B-x-7%7D%7B4%7D%5C%5C4y%3D-x-7%5C%5Cx%2B4y%3D-7)
The equation of the line in the form Ax+By=C is ![\mathbf{ x+4y=-7}](https://tex.z-dn.net/?f=%5Cmathbf%7B%20x%2B4y%3D-7%7D)