Which graph represents the linear function below? y-4= (4/3)(x-2)
1 answer:
Answer:
The graph in the attached figure
Step-by-step explanation:
we have
This is the equation of a line into point slope form
The point is (2.4)
The slope is m=4/3
To plot the line find the intercepts
The y-intercept is the value of y when the value of x is equal to zero
For x=0
y-4=(4/3)(0-2)
y=(-8/3)+4
y=4/3
The x-intercept is the value of x when the value of y is equal to zero
0-4=(4/3)(x-2)
-4=(4/3)x-(8/3)
Multiply by 3 both sides
-12=4x-8
4x=8-12
x=-1
we have the points
(2,4), (0,4/3),(-1,0)
Plot the line
Note With only two points it was necessary to draw the line. The third point was calculated for didactic purposes.
see the attached figure
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By definition, two angles are supplementary if the sum of them is 180 degrees. In this case (see figure attached with the answer) the line AD is transversal to lines AB and DC. This is a proof of the Same-side interior angle theorem.
This theorem states that if we have two lines that are parallel and we intercept those two lines with a line that is transversal to both, same-side interior angles are formed, and also sum 180º, in other words, they are supplementary angles.
Then:
By the definition of a parallelogram, AB∥DC. AD is a transversal between these sides, so ∠A and ∠D are <em><u>same-side interior angles</u></em>. Because AB and DC are <em><u>parallel</u></em>, the same-side interior angles must be <em><u>supplementary</u></em> by the same-side interior angles theorem. Therefore, ∠A and ∠D are supplementary.
