Question

Find the equation of the line that passes through points A and B.
A (1,7)
B (-3,-1)​

Answer 1

Equation of a line is -> m= y2 - y1 all over x2 - x1. Therefore, -1 - 7= -8 and -3 - 1= -4. -8 divide -4= 2 so the gradient is 2.

Answer 2

y = 2x + 5

Explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Calculate m using the slope formula

m = (y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = A(1, 7) and (x₂, y₂ ) = B(- 3, - 1)

m =
`(-1-7)/(-3-1)` =
`(-8)/(-4)` = 2, thus

y = 2x + c ← is the partial equation

To find c substitute either of the 2 points into the partial equation.

Using (1, 7), then

7 = 2 + c ⇒ c = 7 - 2 = 5

y = 2x + 5 ← equation of line