Question

Given the conditions (-1,7) and parallel to the line (8x - 3y - 2 = 0), write an equation for the line passing through (-1,7).

a) (8x - 3y + 23 = 0)

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

c) (8x - 3y - 2 = 0)

d) (8x - 3y - 23 = 0)

Answer 1

The equation of the line passing through (-1,7) and parallel to the given line (8x - 3y - 2 = 0) is 8x - 3y + 23 = 0.

Step-by-step explanation:

To find the equation of a line parallel to the given line and passing through the point (-1,7), we need to determine the slope of the given line and then use that slope to write the equation of the parallel line. The slope of the given line is the coefficient of x divided by the coefficient of y, so in this case, the slope is 8/(-3) = -8/3. Since the parallel line has the same slope, the equation of the parallel line will have the form y = mx + b, where m is the slope. Substituting the coordinates of the point (-1,7), we get 7 = (-8/3)(-1) + b. Solving for b, we find b = 7 - 8/3 = 23/3. Therefore, the equation of the line passing through (-1,7) and parallel to the given line (8x - 3y - 2 = 0) is 8x - 3y + 23 = 0.