Answer:
We conclude that the equation in slope-intercept form for this line will be:
[tex]y\:=\:\frac{-5}{4}x+2[/tex]
Step-by-step explanation:
Given
We know that the slope-intercept form of the line equation is
[tex]y=mx+b[/tex]
where m is the slope and b is the y-intercept
Using the slope-intercept form to find the y-intercept 'b'
substituting m = -5/4 and the point (-4, 7)
[tex]y = mx+b[/tex]
[tex]7=\:\frac{-5}{4}\left(-4\right)+b[/tex]
[tex]-\left(-5\right)+b=7[/tex]
[tex]5+b=7[/tex]
subtract 5 from both sides
[tex]5+b-5=7-5[/tex]
[tex]b=2[/tex]
now substituting b = 2 and m = -5/4 in the slope-intercept form
[tex]y = mx+b[/tex]
[tex]y\:=\:\frac{-5}{4}x+2[/tex]
Therefore, we conclude that the equation in slope-intercept form for this line will be:
[tex]y\:=\:\frac{-5}{4}x+2[/tex]
