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# What is the equation of a line that passes through...

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What is the equation of a line that passes through the point (8, 1) and is perpendicular to the line whose equation is y = −2/3x + 5?

Dec 11, 2017

#1
+8394
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The slope of the line    y  =  -$$\frac23$$x + 5    is   -$$\frac23$$

And the slope of a perpendicular line is the negative reciprocal of  - $$\frac23$$ , which is  $$\frac32$$  .

Using the point  (8, 1)  and the slope  $$\frac32$$ , the equation of our line in point-slope form is...

y - 1  =  $$\frac32$$(x - 8)    This equation is correct as is, but if you need it in slope-intercept form,

distribute the  $$\frac32$$  to both terms in parenthesees.

y - 1  =  $$\frac32$$x - 12

Add  1  to both sides of the equation.

y  =  $$\frac32$$x - 11

Dec 11, 2017

#1
+8394
+1

The slope of the line    y  =  -$$\frac23$$x + 5    is   -$$\frac23$$

And the slope of a perpendicular line is the negative reciprocal of  - $$\frac23$$ , which is  $$\frac32$$  .

Using the point  (8, 1)  and the slope  $$\frac32$$ , the equation of our line in point-slope form is...

y - 1  =  $$\frac32$$(x - 8)    This equation is correct as is, but if you need it in slope-intercept form,

distribute the  $$\frac32$$  to both terms in parenthesees.

y - 1  =  $$\frac32$$x - 12

Add  1  to both sides of the equation.

y  =  $$\frac32$$x - 11

hectictar Dec 11, 2017