+166 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?
+24 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 \(\boxed{\frac{4}{5}}\)
+129852 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....
