Question

1. a) Determine the equation of the line in slope y-intercept form that runs

through points (12,-7) and (-8,3).
b) Line is perpendicular to the line from part a) and has the same
y-intercept as 5x-6y + 54 = 0. State the equation of line in standard form.

Answer 1

a)

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

b)

`2x - y = - 9`

Explanation:

a)

`m = (3 - ( - 7))/( - 8 - 12) = (10)/( - 20) = - (1)/(2)`

`- 7 = - (1)/(2) (12) + b`

`- 7 = - 6 + b`

`b = - 1`

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

b) Slopes of perpendicular lines are negative reciprocals of each other, so if the original line has slope -1/2, the perpendicular line will have a slope of 2.

`5x - 6y + 54 = 0`

`5x - 6y = - 54`

We see that the y-intercept of this line is at (0, 9), so in slope-intercept form, we have

`y = 2x + 9`

Putting this in standard form:

`- 2x + y = 9`

`2x - y = - 9`