Math CentralQuandaries & Queries


Question from Hanna, a student:

The problem says, "Write the equation in standard form for the line that is perpendicular to the graph of y=5x+1 with a y-intercept of 4." I have no clue how to do this. Please help me!

Hi Hanna,

I am not sure what your text means by "standard form" but I am going to use the slope-intercept form $y = mx + b$ where $m$ is the slope and $b$ is the y-intercept. You know that the y-intercept is 4 so the equation of the line is $y = mx + 4$ and all you need to determine is the slope.

Since the given line $y = 5x + 1$ is also in slope-intercept form you know its slope is 5. The fact you need to complete the problem is that if two lines with slopes $m$ and $n$ are perpendicular then $m = \large \frac{-1}{n}.$


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