Line B represents the given linear equation [tex]-3y =15 -4x.[/tex]
Slope intercept form is [tex]y = \frac{4}{3}x-5[/tex]
y-intercept is -5.
Slope of the line is [tex]\frac{4}{3}[/tex].
What is linear equation?
" Linear equation is defined as the algebraic expression whose highest exponent of the variable is 1."
Formula used
Slope = [tex]\frac{y_{2}-y_{1} }{x_{2} -x_{1} }[/tex]
Slope intercept form y=mx +c
c = y-intercept
m = slope
According to the question,
Given linear equation,
[tex]-3y = 15-4x[/tex]
Convert the given linear equation in slope intercept form we get,
[tex]y = \frac{4}{3}x-5[/tex]
Compare it with the formula we get,
Slope 'm' = [tex]\frac{4}{3}[/tex]
y-intercept = -5
From the diagram we can have coordinates of line B
[tex]( x_{1} ,y_{1} )= (3,-1)\\\\( x_{2} ,y_{2} )= (0,-5)[/tex]
Substitute the value to get slope of line B,
Slope of line 'B' = [tex]\frac{(-5-(-1))}{0-3}[/tex]
[tex]= \frac{-4}{-3} \\\\=\frac{4}{3}[/tex]
From the diagram y-intercept for line B is -5.
Equation of line B
[tex]y = \frac{4}{3}x-5[/tex]
Hence, slope intercept form is [tex]y = \frac{4}{3}x-5[/tex]. Line B represents the given equation with y-intercept is -5 , Slope of the line is [tex]\frac{4}{3}[/tex].
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