Question

Line n passes through the points (-3,-7.5) and (2,-5). Tahila determined that the equation of line n is y = 0.5x. Explain the error Tahila made while determining her equation. Be sure to include the correct equation in your explanation.

Answer 1

She omitted the y- intercept

Explanation:

The equation of a line in slope- intercept form is

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

To calculate m use the slope formula

m = (y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = (- 3, - 7.5) and (x₂, y₂ ) = (2, - 5)

m =
`(-5+7.5)/(2+3)` =
`(2.5)/(5)` = 0.5, thus

y = 0.5x + c ← is the partial equation

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

Using (2, - 5), then

- 5 = 1 + c ⇒ c = - 5- 1 = - 6

y = 0.5x - 6 ← equation if line