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The x-intercept of a positively-sloped line is -5, and the area of the triangle formed by the line, the x-axis, and the y-axis is 10. What is the slope of the line?

 Jan 5, 2019
 #1
avatar+24 
+1

The x-intercept refers to when y=0. 

 

Also, since the x-intercept is -5, then that means one of the legs of the right triangle is 5. 

 

Using the formula for the area of a triangle, \(\frac{5h}{2}=10 \rightarrow 5h=20 \rightarrow h=4\)

 

Now you have 2 points, (-5, 0) and (0, 4) (using (0, -4) also works i think)

 

Find the slope to be \(\boxed{\frac{4}{5}}\)

.
 Jan 5, 2019
 #2
avatar+98107 
+1

A slight correction for asdf's answer......the second point is  (4, 0)

 

And the slope of the line is  [ -5 - 0 ] / [ 0 - 4] = -5 / -4 =   5 /4    ....just as asdf found !!!!

 

Also  (-4, 0)  can't be an alternative solution because this would mean that the line has a negative slope....

 

 

cool cool cool

 Jan 6, 2019

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