Question

A line passes through the points (2,-4) and (6,10). What is the equation of the line?

Answer 1

Answer:

y = $\frac{7}{2}$ x - 11

Step-by-step 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 = $\frac{y_{2}-y_{1} }{x_{2}-x_{1} }$

with (x₁, y₁ ) = (2, - 4) and (x₂, y₂ ) = (6, 10)

m = $\frac{10+4}{6-2}$ = $\frac{14}{4}$ = $\frac{7}{2}$ , thus

y = $\frac{7}{2}$ x + c ← is the partial equation

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

Using (2, - 4) , then

- 4 = 7 + c ⇒ c = - 4 - 7 = - 11

y = $\frac{7}{2}$ x - 11 ← equation of line