Question

5 Write the equation of a line that is parallel to y =-5/4x + 7 and that passes through the point (-4,1).

Answer 1

The equation of the line is given as y = mx + b in slope-intercept form, where m is the slope and b is the y-intercept.

Therefore;

$\begin{gathered} y=mx+b \\ \text{When x=-4 and y=1, the parallel equation is;} \\ 1=-\frac{5}{4}(-4)+b \\ 1=\frac{20}{4}+b \\ 1=5+b \\ 1-5=b \\ b=4 \end{gathered}$

Having determined the y-intercept as 4 for the coordinates (-4, 1), and having in mind that lines that are parallel have the same slope, then;

$\begin{gathered} y=mx+b \\ y=-\frac{5}{4}x+4 \end{gathered}$

The equation of the parallel line that passes through the point (-4, 1) is derived as y = -5/4x + 4