Question

choose the equation that has solutions (5, 7) and (8, 13).
a. $3x - y = 8$
b. $y = x + 2$
c. $y - x = 5$
d. $y = 2x - 3$
from unit 3, lesson 9
a length of ribbon is cut into two pieces to use in a craft project. the graph shows the length (in feet) of the second piece, $x$, for each length of the first piece, $y$.

Explanation:

Step1: Test option A with (5,7)

Substitute \(x = 5\), \(y = 7\) into \(3x - y\): \(3\times5 - 7 = 15 - 7 = 8\). Now test with (8,13): \(3\times8 - 13 = 24 - 13 = 11
eq8\). So A is wrong.

Step2: Test option B with (5,7)

Substitute \(x = 5\) into \(y = x + 2\): \(y = 5 + 2 = 7\) (good for (5,7)). Test with (8,13): \(y = 8 + 2 = 10
eq13\). So B is wrong.

Step3: Test option C with (5,7)

Substitute \(x = 5\), \(y = 7\) into \(y - x\): \(7 - 5 = 2
eq5\). So C is wrong.

Step4: Test option D with (5,7)

Substitute \(x = 5\) into \(y = 2x - 3\): \(y = 2\times5 - 3 = 10 - 3 = 7\) (good for (5,7)). Test with (8,13): \(y = 2\times8 - 3 = 16 - 3 = 13\) (good for (8,13)).

Answer:

D. \(y = 2x - 3\)