Answer
Point-slope form is y - 7 = 3/4 (x + 8)
General form is y = (3/4)x + 13
Step-by-step explanation
Given equation: 3x - 4y -7 = 0
Rewriting the equation in gradient intercept form, we have
3x - 7 = 4y
⇒ 4y = 3x - 7
Divide through by 4
4y/4 = 3x/4 - 7/4
y = (3/4)x - 7/4
The gradient of the line of the equation; m₁ = 3/4
Since the lines are parallel, they will have the same gradient.
Let the gradient of the line that passes through (-8, 7) = m₂
∴ m₁ = m₂ = 3/4
Using gradient in one point form: m = (y - y₁)/(x - x₁)
Note: (x₁, y₁) = (-8, 7)
⇒ 3/4 = (y - 7)/(x - -8)
y - 7 = 3/4(x + 8)
Hence, the equation for the line in point-slope form is y - 7 = 3/4 (x + 8)
For the general form,
4(y - 7) = 3(x + 8)
4y - 28 = 3x + 24
4y = 3x + 24 + 28
4y = 3x + 52
To simplify, divide through by 4
y = (3/4)x + 13
The general form for the equation of the line is y = (3/4)x + 13