Question

Write a linear equation that is parallel to

5x + 2y = -8 and passes through the point
(8,-9).

Answer 1

To create a linear equation parallel to 5x + 2y = -8 that goes through (8,-9), find the slope of the given line, use that same slope, and apply the point-slope equation with the given point to get the final equation y = -2.5x + 11.

Step-by-step explanation:

To write a linear equation that is parallel to the given equation 5x + 2y = -8 and passes through the point (8,-9), we need to follow these steps:

1. Find the slope of the given line by rewriting it in slope-intercept form (y = mx + b).
2. Use the slope obtained from the original line since parallel lines have the same slope.
3. Plug the slope and the coordinates of the given point into the point-slope form of the equation y - y1 = m(x - x1) to find the equation of our line.

First, we arrange 5x + 2y = -8 into slope-intercept form, yielding y = -2.5x - 4. This means the slope (m) is -2.5. Second, because parallel lines have the same slope, our new line will also have a slope of -2.5. Finally, we use the point-slope form with our point (8,-9): y - (-9) = -2.5(x - 8). Simplifying, we get y + 9 = -2.5x + 20, and then y = -2.5x + 11 as our final equation. This equation has a slope of -2.5 and passes through (8,-9), making it parallel to the original line.

Answer 2

2y=11 - 5x

Step-by-step explanation:

An equation that is parallel shares the same gradient thus

2y= -5x - 8

y = -5/2x- 4

gradient m = -5/2

substitute value of m and the co-ordinates into a new linear equation

y = mx + c

-9 = (-5/2)(8) + c

c = 20-9 = 11

thus y = -5/2x + 11

2y=11 - 5x