Question

Write the equation of the line that passes through (1,8) and (3, 3). Write it in slope-intercept form.

Answer 1

Answer:

y = - $\frac{5}{2}$ x + $\frac{21}{2}$

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, 8) and (x₂, y₂ ) = (3, 3)

m = $\frac{3-8}{3-1}$ = - $\frac{5}{2}$ , thus

y = - $\frac{5}{2}$ x + c ← is the partial equation

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

Using (1, 8), then

8 = - $\frac{5}{2}$ + c ⇒ c = 8 + $\frac{5}{2}$ = $\frac{21}{2}$

y = - $\frac{5}{2}$ x + $\frac{21}{2}$ ← equation of line