Question

Find the equation of a line that passes through the points (1,-5) and (3,-6).

Answer 1

Answer:

y = - $\frac{1}{2}$ x - $\frac{9}{2}$

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 ) = (1, - 5) and (x₂, y₂ ) = (3, - 6)

m = $\frac{-6+5}{3=2}$ = - $\frac{1}{2}$ , then

y = - $\frac{1}{2}$ x + c ← is the partial equation

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

Using (1, - 5 ) , then

- 5 = - $\frac{1}{2}$ + c ⇒ c = - 5 + $\frac{1}{2}$ = - $\frac{9}{2}$

y = - $\frac{1}{2}$ x - $\frac{9}{2}$ ← equation of line