The points (1,-23) and (6,r) lie on a line with slope 4. Find the missing coordinate r.
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Answer:
Step-by-step explanation:
You can observe in the figure two parallel lines that are intersected by a transversal and several angles are formed.
The angles m∠3 and m∠6 are located inside the parallel lines and on one side of the transversal, this angles are known as "Consecutive interior angles" and they are supplementary (which means that they add up 180°).
Therefore, you know that:
So you can substitute m∠3=130° and solve for m∠6. Then you get:
For this case we have the following system of equations:
Equating both equations we have:
We must find the solutions, for this we factor. We look for two numbers that, when multiplied, result in 4 and when added, result in 5. These numbers are 4 and 1:
Then, the factorized equation is of the form:
Thus, the solutions are:
We look for solutions for the variable "y":
Thus, the system solutions are given by:
ANswer: