Question

98 points please help with math:

What is the equation of a line that is parallel to y=5/6x − 10 and passes through (12, 8) ?

Answer 1

`\displaystyle y _{ \text{parallel}} = (5)/(6) x- 2`

Explanation:

we are given a equation of line

`\displaystyle y = (5)/(6) x - 10`

we want to figure out the line Parallel to the given line and passes through (12,8)

to figure out the parallel line we need to figure out two things one is the Slope of the parallel line another is the y-intercept of the parallel line

figuring out the slope of the parallel line is easy because we know that parallel lines have the same slope therefore,

`\displaystyle m _{ \text{parallel}} = (5)/(6)`

now we need to figure out the y-intercept and the equation to do so we can consider the following formula:

`\displaystyle y - y_(1) = m(x - x_(1))`

we the point where the parallel line passes i.e
`(x_1,y_1)=(12,8)` and we already got that the slope is ⅚ thus substitute:

`\displaystyle y - 8= (5)/(6) (x- 12)`

we can figure out the equation by simplifying the above equation to slope-intercept form in order to do so

distribute:

`\displaystyle y - 8= (5)/(6) x- (5)/(6) * 12`

reduce fraction:

`\displaystyle y - 8= (5)/(6) x- 5 * 2`

simplify multiplication:

`\displaystyle y - 8= (5)/(6) x- 10`

add 8 to both sides:

`\displaystyle y = (5)/(6) x- 2`

and we are done!