Line $$k$$ has a slope of $$-5$$. Line $$j$$ is perpendicular to line $$k$$ and passes through the point $$(5,9)$$.

Create the equation for line $$j$$.



<div id="id_cont_display" class="markdown-body editormd-html-preview"><textarea>Line $$k$$ has a slope of $$-5$$. Line $$j$$ is perpendicular to line $$k$$ and passes through the point $$(5,9)$$.

Create the equation for line $$j$$.

</textarea>Line <math><semantics><mrow><mi>k</mi></mrow><annotation encoding="application/x-tex">k</annotation></semantics></math>k has a slope of <math><semantics><mrow><mo>−</mo><mn>5</mn></mrow><annotation encoding="application/x-tex">-5</annotation></semantics></math>−5. Line <math><semantics><mrow><mi>j</mi></mrow><annotation encoding="application/x-tex">j</annotation></semantics></math>j is perpendicular to line <math><semantics><mrow><mi>k</mi></mrow><annotation encoding="application/x-tex">k</annotation></semantics></math>k and passes through the point <math><semantics><mrow><mo>(</mo><mn>5</mn><mo separator="true">,</mo><mn>9</mn><mo>)</mo></mrow><annotation encoding="application/x-tex">(5,9)</annotation></semantics></math>(5,9).
Create the equation for line <math><semantics><mrow><mi>j</mi></mrow><annotation encoding="application/x-tex">j</annotation></semantics></math>j.
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<div id="id_solution_display" class="markdown-body editormd-html-preview"><textarea>Line $$k$$ has a slope of $$-5$$. Line $$j$$ is perpendicular to line $$k$$. the slope of $$j$$ is $$\frac{1}{5}$$.

The equation of the line $$j$$ is

$$y-9=\frac{1}{5}(x-5)$$ 

or, $$5 y-45=x-5$$

or, $$x-5 y+40=0$$

</textarea>Line <math><semantics><mrow><mi>k</mi></mrow><annotation encoding="application/x-tex">k</annotation></semantics></math>k has a slope of <math><semantics><mrow><mo>−</mo><mn>5</mn></mrow><annotation encoding="application/x-tex">-5</annotation></semantics></math>−5. Line <math><semantics><mrow><mi>j</mi></mrow><annotation encoding="application/x-tex">j</annotation></semantics></math>j is perpendicular to line <math><semantics><mrow><mi>k</mi></mrow><annotation encoding="application/x-tex">k</annotation></semantics></math>k. the slope of <math><semantics><mrow><mi>j</mi></mrow><annotation encoding="application/x-tex">j</annotation></semantics></math>j is <math><semantics><mrow><mfrac><mrow><mn>1</mn></mrow><mrow><mn>5</mn></mrow></mfrac></mrow><annotation encoding="application/x-tex">\frac{1}{5}</annotation></semantics></math>​5​​1​​.
The equation of the line <math><semantics><mrow><mi>j</mi></mrow><annotation encoding="application/x-tex">j</annotation></semantics></math>j is
<math><semantics><mrow><mi>y</mi><mo>−</mo><mn>9</mn><mo>=</mo><mfrac><mrow><mn>1</mn></mrow><mrow><mn>5</mn></mrow></mfrac><mo>(</mo><mi>x</mi><mo>−</mo><mn>5</mn><mo>)</mo></mrow><annotation encoding="application/x-tex">y-9=\frac{1}{5}(x-5)</annotation></semantics></math>y−9=​5​​1​​(x−5) 
or, <math><semantics><mrow><mn>5</mn><mi>y</mi><mo>−</mo><mn>4</mn><mn>5</mn><mo>=</mo><mi>x</mi><mo>−</mo><mn>5</mn></mrow><annotation encoding="application/x-tex">5 y-45=x-5</annotation></semantics></math>5y−45=x−5
or, <math><semantics><mrow><mi>x</mi><mo>−</mo><mn>5</mn><mi>y</mi><mo>+</mo><mn>4</mn><mn>0</mn><mo>=</mo><mn>0</mn></mrow><annotation encoding="application/x-tex">x-5 y+40=0</annotation></semantics></math>x−5y+40=0
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