Question

Write the equation of the line that is parallel to 2x – 4y = 8 and passes through the point ( -4, 3) in each of the following forms: Point – Slope Form Slope – Intercept Form Standard Form

Answer 1

slope-intercept form: y =
`(1)/(2)x+5`

point-slope form: (y - 3) =
`(1)/(2)`(x + 4)

standard form: x - 2y = -10

Explanation:

Lines that are parallel to each other have the same slope. Using the given line: 2x - 4y = 8, we can solve for slope by converting to slope-intercept form:

-4y = -2x + 8

divide all terms by '-4': y =
`(1)/(2)`x -2

Given a slope of
`(1)/(2)` and point of (-4, 3), we can find the three forms:

point-slope form: (y - 3) =
`(1)/(2)`(x + 4)

slope-intercept form: y = mx + b or 3 = (
`(1)/(2)`)(-4) + b

3 = -2 + b or 5 = b, so y =
`(1)/(2)x+5`

standard form: x - 2y = -10