Question

which ordered pairs represent points on the graph of this equation? select all that apply.
$y = \frac{1}{4}x + 3$
(6, -1) (4, 6) (0, 3)
(-3, -5) (2, 0) (-4, 2)

Explanation:

Step1: Check (6, -1)

Substitute \( x = 6 \) into \( y=\frac{1}{4}x + 3 \): \( y=\frac{1}{4}\times6 + 3=\frac{3}{2}+3=\frac{9}{2}=4.5
eq - 1 \), so (6, -1) is not on the graph.

Step2: Check (4, 6)

Substitute \( x = 4 \) into \( y=\frac{1}{4}x + 3 \): \( y=\frac{1}{4}\times4+3 = 1 + 3=4
eq6 \), so (4, 6) is not on the graph.

Step3: Check (0, 3)

Substitute \( x = 0 \) into \( y=\frac{1}{4}x + 3 \): \( y=\frac{1}{4}\times0+3 = 3 \), so (0, 3) is on the graph.

Step4: Check (-3, -5)

Substitute \( x=-3 \) into \( y=\frac{1}{4}x + 3 \): \( y=\frac{1}{4}\times(-3)+3=-\frac{3}{4}+3=\frac{9}{4}=2.25
eq - 5 \), so (-3, -5) is not on the graph.

Step5: Check (2, 0)

Substitute \( x = 2 \) into \( y=\frac{1}{4}x + 3 \): \( y=\frac{1}{4}\times2+3=\frac{1}{2}+3=\frac{7}{2}=3.5
eq0 \), so (2, 0) is not on the graph.

Step6: Check (-4, 2)

Substitute \( x=-4 \) into \( y=\frac{1}{4}x + 3 \): \( y=\frac{1}{4}\times(-4)+3=-1 + 3=2 \), so (-4, 2) is on the graph.

Answer:

The ordered pairs that represent points on the graph of \( y=\frac{1}{4}x + 3 \) are \((0, 3)\) and \((-4, 2)\).