Question

Find the equation of the line through (5,7) parallel to the line 7x + 5y = 12​

Answer 1

`y -7 = -(7)/(5)(x-5)`

or

`y = -(7)/(5)x +14`

Explanation:

Parallel lines are lines which have the same slope. To write the equation of the line parallel, find the slope of the equation 7x + 5y = 12 through conversion into slope intercept form.

7x + 5y = 12 becomes y = -7/5x + 12/5. The slope is -7/5.

Substitute\ m =-7/5 and the point (5,7) into the slope intercept form.

`y-y_1=m(x-x_1)\\y -7= -(7)/(5)(x - 5)`

Convert the equation to slope intercept form by applying the distributive property.

`y -7 = -(7)/(5)(x-5)\\y -7 = -(7)/(5)x +7\\y = -(7)/(5)x +7+7\\y = -(7)/(5)x +14`