Question

graphing an equation in slope-intercept form
graph ( y = \frac{3}{4}x + 5 )
which point lies on the graph of the line?
( circ ) (5, 8)
( circ ) (1, 6)
( circ ) (-3, 3)
( circ ) (-4, 2)
(the table and graph are part of the problem but their text is as shown in the image description.)

Explanation:

Step1: Test point (5,8)

Substitute $x=5, y=8$ into $y=\frac{3}{4}x+5$:
$\frac{3}{4} \times 5 + 5 = \frac{15}{4} + 5 = \frac{15}{4} + \frac{20}{4} = \frac{35}{4} = 8.75
eq 8$

Step2: Test point (1,6)

Substitute $x=1, y=6$ into $y=\frac{3}{4}x+5$:
$\frac{3}{4} \times 1 + 5 = \frac{3}{4} + 5 = 5.75
eq 6$

Step3: Test point (-3,3)

Substitute $x=-3, y=3$ into $y=\frac{3}{4}x+5$:
$\frac{3}{4} \times (-3) + 5 = -\frac{9}{4} + 5 = -\frac{9}{4} + \frac{20}{4} = \frac{11}{4} = 2.75
eq 3$

Step4: Test point (-4,2)

Substitute $x=-4, y=2$ into $y=\frac{3}{4}x+5$:
$\frac{3}{4} \times (-4) + 5 = -3 + 5 = 2 = 2$

Answer:

(-4, 2)