The equation of the following lines (2,6) (-3,5)

Question

Find the equations of the following lines. Write the equation in the form ax+bx=c

Answer 1

I consider we are looking for the line that contains points (2, 6) and (-3,5). There is exactly one line.

 

We can use point slope formula and transform the equation to have the form desired.

 

We find slope first.

slope = (y₂-y₁)/(x₂-x₁)

slope = (6-5)/(2-(-3))

slope = 1/5.

 

Next, we use the point slope formula.

y-y₁=slope(x-x₁).

y-6=1/5(x-2),

y-6=1/5x-2/5.

 

We change this equation using equivalent transformations to obtain the desired form.

 

1/5x-y =6 2/5.

 

We can get rid of fractions by multiplying this equation by 5.

x - 5y = 32.

a=1, b=-5, c=32.