Question

Find an equation of the line passing through the point (-1,8) and parallel to the line joining the points (-3,4) (4,-1).

Answer 1

Answer:

The equation of the line will be $7y=(-5x)+51$

Step-by-step explanation:

If a line passes through two points (x,y) and (x',y') then slope of the line will be = $\frac{y-y'}{x-x'}$

Now we know the points are (-3,4) and (4,-1) then the slope of the line will be =$\frac{4-(-1)}{(-3-4)}$=$\frac{5}{(-7)} =(-\frac{5}{7}$)

We know that two parallel lines have the same slope then a line which is passing through a point (-1,8)will be =( $-\frac{5}{7}$)

Let the equation of the line is y=mx+c

Then by putting the value of x,y and m we can get the value of c.

$8=(-\frac{5}{7})+c$

$c=8-\frac{5}{7} \\c=\frac{56-5}{7} =\frac{51}{7}$

Then equation will be $y=(-\frac{5}{7})x+\frac{51}{7}$

$7y=(-5x)+51$