Equation of line is [tex]y=\frac{-3}{4}x+\frac{19}{4}[/tex]
Solution:
Given data: slope = [tex]-\frac{3}{4}[/tex] and point (1, 4)
Equation of a line with slope passing through the point formula:
[tex]y-y_1=m(x-x_1)[/tex]
Here, [tex]x_1=1, y_1=4[/tex] and [tex]m=\frac{-3}{4}[/tex]
Substitute these in the formula, we get
⇒ [tex]y-4=-\frac{3}{4} (x-1)[/tex]
⇒ [tex]4(y-4)=-3(x-1)[/tex]
⇒ [tex]4y-16=-3x+3[/tex]
Add 16 on both sides of the equation.
⇒ [tex]4y=-3x+3+16[/tex]
⇒ [tex]4y=-3x+19[/tex]
Divide by 4 on both sides of the equation.
⇒ [tex]y=\frac{-3}{4}x+\frac{19}{4}[/tex]
Hence equation of the line is [tex]y=\frac{-3}{4}x+\frac{19}{4}.[/tex]
Graph of the line is attached below.
