Find an equation for the given line in the form ax+by=​c Through (-8,14); parallel to 7x+4y=17. Need some help. Thanks!!?

First, we convert the given equation to its slope-intercept form in order to

find its slope.

7x + 4y = 17

7x - 7x + 4y = - 7x + 17

4y = - 7x + 17

4y/4 = - 7x/4 + 17/4

y = - 7x/4 + 17/4

Therefore, the slope of the first equation is…

m = - 7/4

Since the required line is specified as being parallel, its slope is the same.

m = - 7/4

Using the point-slope form, we then write…

(y - y0) = m(x - x0)

where…

x0 = - 8

y0 = 14

m = - 7/4

(y - 14) = (- 7/4)[x - (- 8)]

(y - 14) = (- 7/4)(x + 8)

y - 14 = - 7x/4 - 8/4

y - 14 = - 7x/4 - 2

y - 14 + 14 = - 7x/4 - 2 + 14

y = - 7x/4 + 12

That is the slope-intercept form of the required equation. We convert it to

the requested standard form as follows…

y = - 7x/4 + 12

y = - 7x/4 + 48/4

y = (- 7x + 48)/4

4y = 4(- 7x + 48)/4

4y = - 7x + 48

7x + 4y = - 7x + 7x + 48

7x + 4y = 48 ANSWER

This is the standard form.

If it's parallel, it will say

7x + 4y = something.

If it goes through (-8,14),

the "something" must be -56+56 = 0.

So the desired equation is 7x + 4y = 0.