Write the equation, in slope-intercept form , of the line that passes through the point the points (3,-5) and is parallel to 8x-2y=16

Answer 1

1. First, rearrange the given equation 8x - 2y = 16 into slope-intercept form (y = mx + b), where m is the slope and b is the y-intercept:

8x - 2y = 16

-2y = -8x + 16

Divide both sides by -2 to solve for y:

y = 4x - 8

2. Since the line you want is parallel to the line y = 4x - 8, it will have the same slope, which is 4.

3. Now that you know the slope (m = 4) and have a point (3, -5), you can use the point-slope form of the equation of a line:

y - y₁ = m(x - x₁)

Plug in the values from the point (3, -5):

y - (-5) = 4(x - 3)

4. Simplify the equation:

y + 5 = 4(x - 3)

5. Distribute the 4 on the right side:

y + 5 = 4x - 12

6. To isolate y, subtract 5 from both sides:

y = 4x - 12 - 5

7. Simplify the equation further:

y = 4x - 17

So, the equation of the line in slope-intercept form that passes through the point (3, -5) and is parallel to 8x - 2y = 16 is:

y = 4x - 17