Write an equation of the line containing the givin point and parallel to the givin line. Express your answer in the form y=mx+b

The equation of the line is y=?

(-5,9);8x=7y+5

since the new line is parallel, it will differ only in the constant,

that is,
its equation will be 8x = 7y + c
plug in the point (-5,9)
-40 = 63 + c
c = -103
so we have
8x = 7y - 103 , rearrange
8x + 103 = 7y
(8/7)x + 103/7 = y

To find an equation of a line parallel to the given line, we need to know that parallel lines have the same slope.

First, let's rewrite the given equation 8x=7y+5 in the slope-intercept form y=mx+b, where m represents the slope and b represents the y-intercept.

Starting with 8x=7y+5, we can isolate y by subtracting 5 from both sides:
8x - 5 = 7y

Next, we divide both sides by 7 to solve for y:
(8x - 5)/7 = y

Thus, we have the equation in slope-intercept form, y = (8/7)x - 5/7.

Since the new line is parallel to the given line, it has the same slope of 8/7. We can use the given point (-5,9) to find the y-intercept (b) of the new line.

Using the point-slope form of a line, y - y₁ = m(x - x₁), where (x₁, y₁) is the given point, and m is the slope of the line, we substitute the given values:

y - 9 = (8/7)(x - (-5))
y - 9 = (8/7)(x + 5)

Distributing (8/7) to (x + 5):
y - 9 = (8/7)x + (8/7)(5)
y - 9 = (8/7)x + 40/7

Adding 9 to both sides to isolate y:
y = (8/7)x + 40/7 + 9
y = (8/7)x + 40/7 + 63/7
y = (8/7)x + 103/7

Therefore, the equation of the line parallel to 8x=7y+5 and passing through the point (-5,9) is y = (8/7)x + 103/7.