Question

Find the equation of a line that is perpendicular to the line y=1/9x+4 and contains the point (-9,0).​

Answer 1

Equation of a line that is perpendicular to the line $y=1/9x+4$ and contains the point (-9,0). is $y=-9x-81$

Step-by-step explanation:

We need to find the equation of a line that is perpendicular to the line $y=1/9x+4$ and contains the point (-9,0).​

Finding slope

Since the lines are parallel, the slopes will be -1/slope 1

The equation given is in slope-intercept form: $y=mx+b$ where m is slope.

Comparing with given equation $y=1/9x+4$ the slope = 1/9

So, slope of required line is: -9

Finding y-intercept

To find y-intercept we use point (-9,0) and slope -9

Putting values:

$y=mx+b\\0=-9(-9)+b\\0=81+b\\b=-81$

So, y-intercept of required line is -81

Finding equation of required line:

Slope m = -9, y-intercept b = -81

Putting values

$y=mx+b\\y=-9x-81$

So,  equation of a line that is perpendicular to the line $y=1/9x+4$ and contains the point (-9,0). is $y=-9x-81$

Keywords: Equation of line using Slope

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