Question

Write the equation of the line in slope intercept form that passes through the point (3,2) and the the intersection of lines: 2x-3y=24 and 2x+y=8

Answer 1

ANSWER


`\boxed {y = - 2x + 7}`

Step-by-step explanation

We want to write the equation in slope-intercept form for the line that passes through the point (3,2) and the intersection of the lines:


`2x - 3y = 24...(1)`


`2x + y = 8...(2)`

We subtract equation (1) from equation (2) to get,


`y - - 3y = 8 - 24`


`4y = - 16`


`y = - 4`

Put y=-4 into equation (2) to get the value of x.


`2x - 4 = 8`


`2x = 8 + 4`


`2x = 12`


`x = 6`

Therefore the line passes through (3,2) and

(6,-4).

The slope of this line is


`m = ( - 4 - 2)/(6 - 3) = ( - 6)/(3) = - 2`

The slope intercept form is given by the formula,


`y = mx + c`

where m=-2 is the slope.

We substitute the slope to get,


`y = - 2x + c`

We substitute the point (3,2) to find the value of c.


`3 = - 2(2) + c`


`3 = - 4 + c`


`c = 4 + 3 = 7`

Hence the equation in slope-intercept form is


`y = - 2x + 7`