Question

Find the equation of the line through (3,6) which is parallel to the line y=8x−9

Answer 1

The answer is y = 8x - 18, why?

Explanation:

! :: To find the equation of a line that is parallel to the line y = 8x - 9 and passes through the point (3, 6), we can follow these steps:

1. Recall that parallel lines have the same slope. The given line has a slope of 8!

2. 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..

3. Substitute the given values into the equation: y - 6 = 8(x - 3).

4. Distribute 8 to the terms inside the parentheses: y - 6 = 8x - 24.

5. Move the constant term to the other side of the equation: y = 8x - 24 + 6.

6. Simplify the equation: y = 8x - 18.

Therefore, the equation of the line that is parallel to y = 8x - 9 and passes through the point (3, 6) is y = 8x - 18!

Answer 2

y = 8x - 18

Explanation:

Rule #1 is that parallel lines have the same slope. The line given is in y = mx + b form, where m is the slope. So the slope of the line we're trying to find is also m = 8. You're given a point, so all you need to do is use point-slope form and convert it to slope-intercept form if necessary:

y - y1 = m (x - x1)

y - 6 = 8 ( x - 3)

If you need slope-intercept:

y = 8x - 24 + 6

y = 8x - 18