Question

Use the given conditions to write an equation for the line. Passing through (-1,7) and parallel to the line whose equation is 8x - 3y - 2 = 0. The equation of the line is:

a) (8x - 3y - 2 = 0)
b) (8x - 3y + 2 = 0)
c) (8x + 3y - 2 = 0)
d) (8x + 3y + 2 = 0)

Answer 1

The equation of the line passing through the point (-1,7) and parallel to the line 8x - 3y - 2 = 0 is 8x - 3y + 29 = 0.

Step-by-step explanation:

To find the equation of the line passing through (-1,7) and parallel to the line 8x - 3y - 2 = 0, we need to determine the slope of the given line. The slope of a line parallel to a given line is equal to the slope of the given line. Therefore, the slope of the given line is 8/3. We can use the point-slope form of a linear equation, y - y1 = m(x - x1), where (x1, y1) is the given point and m is the slope, to find the equation.

Substituting the given point (-1,7) and the slope 8/3 into the point-slope form, we have y - 7 = (8/3)(x + 1).

Simplifying the equation, we multiply both sides by 3 to eliminate the fraction: 3y - 21 = 8x + 8. Moving the terms around, we get 8x - 3y + 29 = 0.