Question

Find the equation for the linear function that passes through the points (−5,−6) and (10,0). Answers must use whole numbers and/or fractions, not decimals.

Answer 1

Considering the expression of a line, the equation of the line that passes through the pair of points (-5,-6) and (10,0) is y=2/5x -4.

Linear equation

A linear equation o line can be expressed in the form y = mx + b

where

• x and y are coordinates of a point.
• m is the slope.
• b is the ordinate to the origin and represents the coordinate of the point where the line crosses the y axis.

Knowing two points (x₁, y₁) and (x₂, y₂) of a line, the slope m of said line can be calculated using:

m= (y₂ - y₁)÷ (x₂ - x₁)

Substituting the value of the slope m and the value of one of the points in the expression y = mx + b, the value of the ordinate to the origin b can be obtained.

Equation in this case

In this case, being (x₁, y₁)= (-5, -6) and (x₂, y₂)= (10,0), the slope m can be calculated as:

m= (0 - (-6))÷ (10 - (-5))

m= (0 +6)÷ (10 + 5)

m= 6÷ 15

m= 2/5

Considering point 2 and the slope m, you obtain:

0= 2/5×10 + b

0= 4 +b

0 -4= b

-4= b

Finally, the equation of the line is y=2/5x -4.

Answer 2

see explanation

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 ) = (- 5, - 6) and (x₂, y₂ ) = (10, 0)

m =
`(0+6)/(10+5)` =
`(6)/(15)` =
`(2)/(5)`, hence

y =
`(2)/(5)` x + c ← is the partial equation

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

Using (10, 0), then

0 = 4 + c ⇒ c = 0 - 4 = - 4

y =
`(2)/(5)` x - 4 ← equation of line