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AlladinOne [14]
3 years ago
15

The slope of a line is -4 and it’s y-intercept is (0,4) what is the equation of the line that is perpendicular to the first line

and passes through (-8,2)
Mathematics
1 answer:
Rasek [7]3 years ago
4 0

Original line equation: y=-4x+4

Perpendicular lines have opposite reciprocals, so the slope of the perpendicular line would be 1/4x.

Perpendicular line equation: y=1/4x+b

Plug in the coordinates that the line passes through to solve for b. Plug -8 in for x and 2 in for y.

2=1/4(-8)+b

Multiply.

2=-2+b

Add 2 to both sides.

4=b

Equation of the perpendicular line: y=1/4x+4

Hope this helps! :)

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Slope of the line passing through two points <span><span>P=<span>(<span><span>x1</span>,<span>y1</span></span>) </span></span></span>and <span><span>Q=<span>(<span><span>x2</span>,<span>y2</span></span>)</span></span></span> is given by <span><span>m=<span><span><span>y2</span>−<span>y1/</span></span><span><span>x2</span>−<span>x1</span></span></span></span></span>.

We have that <span><span><span>x1</span>=−8</span></span>, <span><span><span>y1</span>=−3</span></span>, <span><span><span>x2</span>=−3</span></span>, <span><span><span>y2</span>=4</span></span>.

Plug given values into formula for slope: <span><span>m=<span><span><span>(4)</span>−<span>(<span>−3</span>)/</span></span><span><span>(<span>−3</span>)</span>−<span>(<span>−8</span>)</span></span></span>=<span>7/5</span></span></span>.

Now y-intercept is <span><span>b=<span>y1</span>−m⋅<span>x1</span></span></span> .

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Finally, equation of the line can be written in the form <span><span>y=mx+b</span></span>.

<span><span>y=<span>7/5</span>x+<span>41/5</span></span></span>

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