Use the table below and write an equation to show the relationship between x and y
2 answers:
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AO is a line segment containing the radii of both circles, which are AK and OE, so AO = AK + OE = 9.
Extend AO to a point P on the line KE. Then we get two similar triangles APK and OPE. Let be the length of KE,
the length of EP, and
the length of OP.
By similarity, we have
OPE is a right triangle, so
Now,
and we also have
Substituting this into the expression containing gives us an equation that we can solve for
:
Answer:
Step-by-step explanation:
(x1, y1) = (5, 4)
(x2, y2) = (0, 2)
First, find the slope. The slope formula is:
I marked the 2 points above in that form, so you can plug those in here:
The slope of this line is 2/5. Next, you can use that slope and whichever known point you want to find the y-intercept. Slope-intercept form is:
where m is the slope and b is the y-intercept.
Plug in the slope we found for m and whichever point you want for (x, y):
Now, solve for b:
In this particular case, there wasn't much to be done. We already had a point at x = 0, and that is already our y-intercept. For similar problems though, that's how you would do it.
Finally, with both the slope and the y-intercept, you can write the equation:
