Respuesta :
Answer:
y = 3/4x -31/4
Step-by-step explanation:
The slope-intercept form of the equation of a line that passes through (5, -4) and has a slope of `3/4 is [tex]y = \frac{3}{4}x + \frac{-31}{4}[/tex]
Solution:
Given that line passes through (5, -4)
Slope "m" = [tex]\frac{3}{4}[/tex]
We have to find the slope intercept form
The slope intercept form is given as:
y = mx + b ---- eqn1
where "m" is the slope of the line and "b" is the y-intercept
Here in this sum m = [tex]\frac{3}{4}[/tex]
Calculating y-intercept:
Substitute (x, y) = (5, -4) and "m" value in eqn 1, we get
[tex]\begin{array}{l}{-4=\frac{3}{4}(5)+b} \\\\ {-4=\frac{15+4 b}{4}} \\\\ {-16=15+4 b} \\\\ {4 b=-31} \\\\ {b=\frac{-31}{4}}\end{array}[/tex]
Now eqn 1 becomes,
[tex]y = \frac{3}{4}x + \frac{-31}{4}[/tex]
Hence the slope intercept form is [tex]y = \frac{3}{4}x + \frac{-31}{4}[/tex]
