Question

question 9 of 22
which of the following is the equation of a line parallel to the line y=4x+1, passing through the point (5,1)?

a. 4x + y = 19
b. 4x - y = 19
c. -4x - y = 19
d. 4x + y = -19

Explanation:

Step1: Determine the slope of the parallel line

The given line is \( y = 4x + 1 \), which is in slope - intercept form \( y=mx + b \) where \( m \) is the slope. So the slope \( m \) of the given line is \( 4 \). Since parallel lines have the same slope, the line we are looking for also has a slope of \( 4 \).

Step2: Use the point - slope form to find the equation of the line

The point - slope form of a line is \( y - y_1=m(x - x_1) \), where \( (x_1,y_1)=(5,1) \) and \( m = 4 \).
Substitute the values into the point - slope form:
\( y - 1=4(x - 5) \)
Expand the right - hand side: \( y-1 = 4x-20 \)
Rearrange the equation to get it in standard form (\( Ax+By = C \)):
\( 4x-y=20 - 1 \)
\( 4x - y=19 \)

We can also check by substituting the point \( (5,1) \) into each option:

• For option A: \( 4(5)+1=20 + 1=21

eq19 \)

• For option B: \( 4(5)-1=20 - 1 = 19 \), which satisfies the equation.
• For option C: \( - 4(5)-1=-20 - 1=-21

eq19 \)

• For option D: \( 4(5)+1=20 + 1 = 21

eq - 19 \)

Answer:

B. \( 4x - y = 19 \)