Randolph is creating parallelogram WXYZ so that WX has an equation of y = 1 over 4x − 6. Segment YZ must pass through the point (−1, 5). Which of the following is the equation for YZ? y − 5 = 1 over 4(x − (−1))
y − (−1) = 1 over 4(x − 5)
y − 5 = −4(x − (−1))
y − (−1) = −4(x − 5)

  y − 5 = 1 over 4(x − (−1))

Step-by-step explanation:

The slope of YZ is the same as the slope of WX, 1/4. Using that, and the given point (-1, 5) in the point-slope form of the equation of a line, we have ...

  y - k = m(x -h) . . . . . line with slope m through point (h, k)

  y -5 = 1/4(x -(-1)) . . . . . . matches the first choice

5x + 3y = - 4

step-by-step explanation:

the equation of a line in standard form is

ax + by = c ( a is a positive integer and b, c are integers )

express the line first of all in slope- intercept form

y = mx + c ( m is the slope and c the y-intercept )

to calculate m use the gradient formula

m = ( y₂ - y₁ ) / ( x₂ - x₁ )

with (x₁, y₁ ) = (7, - 3) and (x₂, y₂ ) = (4, - 8)

m = = -

y = - x + c ← is the partial equation

to find c substitute either of the 2 points into the partial equation

using (4, - 8 ), then

- 8 = - + c ⇒ c = -

y = - x - ← in slope-intercept form

multiply all terms by 3 to eliminate the fractions

3y = - 5x - 4 ( add 5x to both sides )

5x + 3y = - 4 ← in standard form