What is the equation of the line that is parallel to the line y − 1 = 4(x + 3) and passes through the point (4, 32)?

Mathematics

2 answers:

Sav [38]4 years ago

4 0

Your equation is y= 4x + 16

soldi70 [24.7K]4 years ago

4 0

Parallel lines refers to a pair of straight lines that never intercept or touch each other. The slopes of this lines is the same one.

On this exercise is given the equation of a line and a point, and is asked to find the equation of a line in slope-intercept form that is parallel to the given one, and that passes through the given point.

y-1=4(x+3) Distribute the parenthesis
y-1=4x+12 Add 1 in both sides to isolate y
y=4x+13

The slope of the given line is 4, which means that the slope of a line parallel to this one, have to be 4. Now you need to find the value of b or the y-intercept by substituting the given point into the slope-intercept form y=mx+b, where the letter m represents the slope.

y=mx+b Substitute the values of the given point and slope
32=4(4)+b Combine like terms
32=16+b Subtract 16 in both sides to isolate b
16=b

The equation is slope-intercept form for the line that passes through the point (4,32) and is parallel to the given line is y=4x+16.

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