Question

Which equation represents the line that passes through the points (2, 4) and (1, -3)?

y = -x + 6
y = -7x + 18
y = 7x -10
y = x + 2

Answer 1

y = 7x - 10

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 ) = (2, 4) and (x₂, y₂ ) = (1, - 3)

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

y = 7x + c ← is the partial equation

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

Using (2, 4), then

4 = 14 + c ⇒ c = 4 - 14 = - 10

y = 7x - 10 ← equation of line