Answer:
The equation of required line is [tex]y-7=\dfrac{3}{4}(x+1)[/tex]
or [tex] y=\dfrac{3}{4}x+\dfrac{31}{4}[/tex]
Step-by-step explanation:
Required equation is parallel to [tex]y=\dfrac{3}{4}x-4[/tex] this line.
As we know the slope of parallel line is equal.
Slope of given line is [tex]\dfrac{3}{4}[/tex]
Thus, Slope of required line, [tex]m=\dfrac{3}{4}[/tex]
Passing point: (-1,7)
Now, we have one point and slope of equation. Using point slope form of line to find the equation of required line.
Point Slope form of line, [tex]y-y_1=m(x-x_1)[/tex]
[tex]y-7=\dfrac{3}{4}(x-(-1))[/tex]
[tex]y-7=\dfrac{3}{4}(x+1)[/tex]
Hence, The equation of required line is [tex]y-7=\dfrac{3}{4}(x+1)[/tex]
or [tex] y=\dfrac{3}{4}x+\dfrac{31}{4}[/tex]
