Question

linear relationships: end-of-unit assessment
select the 2 answer choices, which are points on the graph of the line $2x + 4y = 20$.
the points are coordinates written $(x,y)$. strategy: think substitution.
a. $(0,5)$
b. $(0,10)$
c. $(1,2)$
d. $(1,4)$
e. $(5,0)$
f. $(10,0)$
a. $2(0) + 4(5) = 20$
$0 + 20 = 20$
true or false (circle one)
b. $2(0) + 4(10) = 20$
$0 + 40 = 20$
true or false (circle one)
c. $2(1) + 4(2) = 20$
$2 + 8 = 20$
true or false (circle one)
d. $2(1) + 4(4) = 20$
$2 + 16 = 20$
true or false (circle one)
e. $2(5) + 4(0) = 20$
$10 + 0 = 20$
true or false (circle one)
f. $2(10) + 4(0) = 20$
$20 + 0 = 20$
true or false (circle one)

Explanation:

To determine which points lie on the line \(2x + 4y = 20\), we substitute the \(x\) and \(y\) values of each point into the equation and check if the equation holds true.

Step 1: Check Point A \((0, 5)\)

Substitute \(x = 0\) and \(y = 5\) into the equation:
\[
2(0) + 4(5) = 0 + 20 = 20
\]
This satisfies the equation, so \((0, 5)\) is on the line.

Step 2: Check Point B \((0, 10)\)

Substitute \(x = 0\) and \(y = 10\) into the equation:
\[
2(0) + 4(10) = 0 + 40 = 40
eq 20
\]
This does not satisfy the equation, so \((0, 10)\) is not on the line.

Step 3: Check Point C \((1, 2)\)

Substitute \(x = 1\) and \(y = 2\) into the equation:
\[
2(1) + 4(2) = 2 + 8 = 10
eq 20
\]
This does not satisfy the equation, so \((1, 2)\) is not on the line.

Step 4: Check Point D \((1, 4)\)

Substitute \(x = 1\) and \(y = 4\) into the equation:
\[
2(1) + 4(4) = 2 + 16 = 18
eq 20
\]
This does not satisfy the equation, so \((1, 4)\) is not on the line.

Step 5: Check Point E \((5, 0)\)

Substitute \(x = 5\) and \(y = 0\) into the equation:
\[
2(5) + 4(0) = 10 + 0 = 10
eq 20
\]
This does not satisfy the equation, so \((5, 0)\) is not on the line.

Step 6: Check Point F \((10, 0)\)

Substitute \(x = 10\) and \(y = 0\) into the equation:
\[
2(10) + 4(0) = 20 + 0 = 20
\]
This satisfies the equation, so \((10, 0)\) is on the line.

Answer:

A. \((0, 5)\), F. \((10, 0)\)