Question

Write the equation of a line that contains (1,5) and (-5,8)

Answer 1

Answer: y =
`-(1)/(2)`x +
`(11)/(2)`

Explanation:

First, we will use the slope formula to find the slope.

`\displaystyle (y_(2) -y_(1) )/(x_(2) -x_(1) ) =(8-5)/(-5-1) =(3)/(-6) =-(1)/(2)`

Next, we will substitute this slope with one of the coordinate points. Then, we will simplify and solve for b to create a slope-intercept form equation by finding the y-intercept.

y = mx + b

y =
`-(1)/(2)`x + b

5 =
`-(1)/(2)`(1) + b

5 =
`-(1)/(2)` + b

5 +
`(1)/(2)` = b

b =
`(11)/(2)`

Lastly, we will substitute this into the equation.

y = mx + b

y =
`-(1)/(2)`x +
`(11)/(2)`

I have attached a graph of the given points and the equation we created.