Write the equation of a line that is parallel to y=-\frac{5}{4}x+7 and tha

Anish Buchanan

Anish Buchanan

Answered question

2021-09-19

Write the equation of a line that is parallel to y=54x+7 and that passes through the point (-4,1).

Answer & Explanation

Macsen Nixon

Macsen Nixon

Skilled2021-09-20Added 117 answers

Step 1
A straight line is a function with equation of the form ax+by=0. This form of equation of a line is called the standard form of equation of a line.
Slope-intercept form of equation of a line is y=mx+c. In this form the slope is m and the y-intercept is equal to (0,c). Two parallel lines have equal slopes.
Step 2
Given equation of a line is y=54x+7.
This is in slope-intercept form so its slope is 54. Required line is parallel to this line and hence has the same slope. So required line's equation in slope-intercept form is: y=54x+c.
The required line passes through the point (−4,1). Substitute this point in the equation and solve for c. Hence, determine the equation of the line.
y=54x+c
1=54(4)+c
1=5+c
c=-4
y=54x4
Hence, required equation of line is y=54x4.

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