Answer:
The equation of line is shown below.
Step-by-step explanation:
The equation of line is
[tex]y+1=\frac{-3}{5}(x-4)[/tex]
It is the point slope form of a line, therefore the slope of the line is [tex]\frac{-3}{5}[/tex] and the line passing through (4,-1).
Rewrite the above equation in slope intercept form.
[tex]y=\frac{-3}{5}x+\frac{12}{5}-1[/tex]
[tex]y=\frac{-3}{5}x+\frac{12-5}{5}[/tex]
[tex]y=\frac{-3}{5}x+\frac{7}{5}[/tex]
The point slope form of a line is
[tex]y=mx+b[/tex]
Where m is the slope and b is y-intercept.
Therefore the slope of the line is [tex]\frac{-3}{5}[/tex] and the y-intercept of the line is [tex]\frac{7}{5}[/tex].
Slope is defined as
[tex]m=\frac{Rise}{Run}[/tex]
Since the slope is negative, therefore the run of the line is considered on the left side. The line rise by 3 and run by 5, therefore we will add 7 in y and subtract 5 from x.
The y-intercept is [tex](0,\frac{7}{5})[/tex].
[tex](0-5,\frac{7}{5}+3)=(-5,\frac{22}{5})=(-5,4.4)[/tex]
Therefore we have three points (4,-1), (-5,4.4) and (0,1.4). Plot the point on the coordinate plane and connect them be a straight line.
