Question

Write an equation of the line containing the given point and parallel to the given line.

(6,-2); 4x - 3y = 8

Answer 1

y = (4/3)x − 10

Explanation:

Rewrite in slope-intercept form.

The slope-intercept form is y = mx + b, where m is the slope and b is they-intercept.

y = mx + b

Subtract 4x from both sides of the equation.

−3y = 8 − 4x

Divide each term by −3 and simplify.

Divide each term in −3y = 8 − 4x by −3.

(−3y/−3)= (8/−3) + (−4x/−3)

Cancel the common factor of −3.

y= (8/−3) + (−4x/−3)

Simplify (8/−3) + (−4x/−3)

y= (4x/3 - 8/3)

Reorder terms.

y= 4x/3 - 8/3

Using the slope-intercept form, the slope is 4/3

m = 4/3

To find an equation that is parallel, the slopes must be equal. Find the parallel line using the point-slope formula.

Use the slope 4/3 and a given point (6, −2) to substitute for
`x_(1)`and
`y_(1)`in the point-slope form.
`y` −
`y_(1)` =
`m` (
`x` −
`x_(1)`) which is derived from the slope equation
`m=` (
`y_(2)`−
`y_(1)`)/(
`x_(2)` -
`x_(1)`)

y − (−2) = (4/3) ⋅ (x − (6))

Simplify the equation and keep it in point-slope form.

y − (−2) = (4/3) ⋅ (x − (6))

solve for y

y = (4/3)x − 10