Y-intercept of the given line is -1.
Slope of the given line is [tex]\frac{3}{4}[/tex] .
Equation of the line in the slope intercept form is [tex]y=\frac{3}{4}x -1[/tex].
" Slope is defined as the ratio of the difference in the change of y-coordinate to the x-coordinate. It represents the inclined plane."
Formula used
[tex]Slope 'm' = \frac{y_{2}-y_{1} }{x_{2} -x_{1} }[/tex]
[tex](x_{1} ,y_{1} ) , (x_{2} ,y_{2} )[/tex] are the points on the line.
Slope intercept form y = mx + b
According to the question,
Given,
Line contains the points
[tex](x_{1} ,y_{1} ) = (4,2)\\(x_{2} ,y_{2} ) = ( 0 , -1)[/tex]
Substitute the value in the formula of slope we get,
[tex]Slope 'm' =\frac{-1-2}{0-4}\\[/tex]
[tex]= \frac{3}{4}[/tex]
Slope 'm' = [tex]= \frac{3}{4}[/tex]
Substitute the value in slope intercept form we get,
[tex]y= \frac{3}{4} x+b[/tex]
Line passing through (0,-1) we get,
[tex]-1= \frac{3}{4} (0)+b[/tex]
⇒[tex]b= -1[/tex]
Y-intercept = -1
Therefore,
Equation of the slope intercept form of the line
[tex]y= \frac{3}{4} x-1[/tex]
Hence, y-intercept = -1. Slope = [tex]\frac{3}{4}[/tex] . Equation of the line in the slope intercept form is [tex]y=\frac{3}{4}x -1[/tex].
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