Question

Find the equation of a line parallel tominus, 4, y, equals, 32, minus, 6, x−4y=32−6xthat passes through the point left bracket, 2, comma, 8, right bracket(2,8).

Answer
Multiple Choice Answers
y, equals, start fraction, 3, divided by, 2, end fraction, x, plus, 5y=
2
3
​
x+5
4, x, plus, 6, y, equals, 564x+6y=56
y, equals, minus, start fraction, 3, divided by, 2, end fraction, x, plus, 5y=−
2
3
​
x+5
6, x, plus, 4, y, equals, 446x+4y=44

Answer 1

The equation of the line parallel to -4y = 32 - 6x and passing through the point (2,8) is y = (3/2)x + 5.

To find the equation of a line parallel to the given equation and passing through the point (2,8), we can follow these steps:

1. First, we need to determine the slope of the given line. The given equation is -4y = 32 - 6x, which can be rearranged to the slope-intercept form y = (3/2)x - 8.

2. The slope of the given line is 3/2. Any line parallel to this line will have the same slope.

3. Now that we have the slope, we can use the point-slope form of a linear equation to find the equation of the parallel line. The point-slope form is given by y - y1 = m(x - x1), where (x1, y1) is the given point and m is the slope.

4. Plugging in the values (2,8) for (x1, y1) and 3/2 for m, we have the equation y - 8 = (3/2)(x - 2).

5. Simplifying, we can distribute (3/2) to (x - 2), resulting in y - 8 = (3/2)x - 3.

6. Finally, we can rearrange the equation to the slope-intercept form y = (3/2)x - 3 + 8, which simplifies to y = (3/2)x + 5.

Therefore, the equation of the line parallel to -4y = 32 - 6x and passing through the point (2,8) is y = (3/2)x + 5.