Please Help! Brainliest and 50 points. Randolph is trying to find the equation of a line parallel to y = 1/4 x − 6 in slope-intercept form that passes through the point (−1, 5). Which of the following equations will he use? A) y − 5 = 1 over 4 (x − (−1))
B) y − (−1) = 1 over 4 (x − 5)
C) y − 5 = −4(x − (−1))
D) y − (−1) = −4(x − 5)

A) y − 5 = 1 over 4 (x − (−1))

Step-by-step explanation:

info: Slope- intercept form: y= mx+b

The equation of a line parallel to y = 1/4 x − 6 is:

y= 1/4x + b as it has the same slope

Since it  passes through the point (−1, 5), we can find intercept:

5= 1/4*(-1) +b b= 5 +1/4

then the equation is:

y= 1/4x +5 1/4

We can test the answer choices for similarity with the above by bringing them to same form:

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

Yes, it has same slope and intercept

B) y- (-1)= 1/4(x-5) ⇒ y= 1/4x - 5/4 +1 ⇒ y= 1/4x - 1/4

No, this has different intercept

C) y- 5= -4(x - (-1)) ⇒ y= -4x + 4 +5 ⇒ y= - 4x =9

No, it has different slope and intercept

D) y − (−1) = −4(x − 5) ⇒ y +1= - 4x +20 ⇒ y= - 4x +19

No, it has different slope and intercept

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