Question

1. a. complete the table with values for x or y that make this equation true: 3x + y = 15.

x	2		6	0	3
y		3				0	8

b. create a graph, plot these points, and find the slope of the line that goes through them.

Explanation:

Step1: Solve for y when x=2

Substitute $x=2$ into $3x+y=15$:
$3(2)+y=15 \implies 6+y=15 \implies y=15-6=9$

Step2: Solve for x when y=3

Substitute $y=3$ into $3x+y=15$:
$3x+3=15 \implies 3x=15-3=12 \implies x=\frac{12}{3}=4$

Step3: Solve for y when x=6

Substitute $x=6$ into $3x+y=15$:
$3(6)+y=15 \implies 18+y=15 \implies y=15-18=-3$

Step4: Solve for y when x=0

Substitute $x=0$ into $3x+y=15$:
$3(0)+y=15 \implies y=15$

Step5: Solve for y when x=3

Substitute $x=3$ into $3x+y=15$:
$3(3)+y=15 \implies 9+y=15 \implies y=15-9=6$

Step6: Solve for x when y=0

Substitute $y=0$ into $3x+y=15$:
$3x+0=15 \implies x=\frac{15}{3}=5$

Step7: Solve for x when y=8

Substitute $y=8$ into $3x+y=15$:
$3x+8=15 \implies 3x=15-8=7 \implies x=\frac{7}{3}$

Step8: Calculate slope using two points

Use points $(2,9)$ and $(4,3)$. Slope formula: $m=\frac{y_2-y_1}{x_2-x_1}$
$m=\frac{3-9}{4-2}=\frac{-6}{2}=-3$

Answer:

Part a: Completed Table

$x$	2	4	6	0	3	5	$\frac{7}{3}$

Part b: Slope

The slope of the line is $\boldsymbol{-3}$
(To graph: plot all the points from the completed table, draw a straight line through them; the line will have a downward slope consistent with the calculated value.)