Answer:
<em>A. y-5 = 1/4(x+1)</em>
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
<em>Hence, the equation that Randolph is trying to find will be y-5 = 1/4(x-(-1)) i.e </em><em>y-5 = 1/4(x+1)</em>
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- 2.1 (Add 2.1 to both sides)