Answer:
The equation of the line in the form Ax+By=C is [tex]\mathbf{ x+4y=-7}[/tex]
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: [tex]y=mx+b[/tex]
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)
[tex]y=mx+b\\0=-\frac{1}{4}(-7)+b\\0= \frac{7}{4}+b\\b=-\frac{7}{4}[/tex]
Now finding the equation of line having slope m= -1/4 and y-intercept b= -7/4
[tex]y=mx+b\\y=-\frac{1}{4}x-\frac{7}{4}[/tex]
Now converting into form Ax+By=C :
[tex]y=-\frac{1}{4}x-\frac{7}{4}\\y=\frac{-x-7}{4}\\4y=-x-7\\x+4y=-7[/tex]
The equation of the line in the form Ax+By=C is [tex]\mathbf{ x+4y=-7}[/tex]
