Randolph is trying to find the equation of a line parallel to y = '1 over 4 x − 6 in slope-intercept form that passes through the point (−1, 5). Which of the following equations will he use? (6 points) y − 5 = 1 over 4 (x − (−1)) y − (−1) = 1 over 4 (x − 5) y − 5 = −4(x − (−1)) y − (−1) = −4(x − 5)

A. y-5 = 1/4(x+1)

Step-by-step explanation:

The equation of a line parallel to the line y = 1/4x - 6 and passing through the point can be expressed in slope-intercept form of the equation

y-y₀ = m(x-x₀) where;

(x₀, y₀) is the given point

m is the slope of the unknown line.

Since the unknown line is parallel to the given line  y = 1/4x - 6, they will have the same slope.

Let us get the slope of the known line  y = 1/4x - 6

Comparing the line  y = 1/4x - 6 with the standard equation of a line  

y = mx + c, the slope of the known line m = 1/4.

The slope of the unknown line is also equivalent to 1/4.

Substituting the given point  (−1, 5) and the calculate slope m into the slope-intercept form of the equation y-y₀ = m(x-x₀);

x₀ = -1, y₀ = 5 and m = 1/4

Hence, the equation that Randolph is trying to find will be y-5 = 1/4(x-(-1)) i.e  y-5 = 1/4(x+1)

x = 3 ± √(5+y)