Question

graph each equation.

1. $y = 5x + 1$
2. $y = 3x + 3$

(there are also some tables and coordinate grids for graphing the equations, and some hand - written notes like $y = 5x + 1$ at the top.)

Explanation:

For Equation 7: $y=5x+1$

Step1: Choose x values, solve for y

Select $x=0,1,2,3$:

• When $x=0$: $y=5(0)+1=1$
• When $x=1$: $y=5(1)+1=6$
• When $x=2$: $y=5(2)+1=11$
• When $x=3$: $y=5(3)+1=16$

Step2: Fill input-output table

Input $(x)$	$5x+1$	Output $(y)$
1	$5(1)+1$	6
2	$5(2)+1$	11
3	$5(3)+1$	16

Step3: Plot points, draw line

Plot $(0,1), (1,6), (2,11), (3,16)$ on the grid, then draw a straight line through them.

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For Equation 9: $y=3x+3$

Step1: Choose x values, solve for y

Select $x=0,1,2,3$:

• When $x=0$: $y=3(0)+3=3$
• When $x=1$: $y=3(1)+3=6$
• When $x=2$: $y=3(2)+3=9$
• When $x=3$: $y=3(3)+3=12$

Step2: Fill input-output table

Input $(x)$	$3x+3$	Output $(y)$
1	$3(1)+3$	6
2	$3(2)+3$	9
3	$3(3)+3$	12

Step3: Plot points, draw line

Plot $(0,3), (1,6), (2,9), (3,12)$ on the grid, then draw a straight line through them.

Answer:

For $y=5x+1$:

Completed table:

Input $(x)$	$5x+1$	Output $(y)$
1	$5(1)+1$	6
2	$5(2)+1$	11
3	$5(3)+1$	16

Graph: Straight line through points $(0,1), (1,6), (2,11), (3,16)$

For $y=3x+3$:

Completed table:

Input $(x)$	$3x+3$	Output $(y)$
1	$3(1)+3$	6
2	$3(2)+3$	9
3	$3(3)+3$	12

Graph: Straight line through points $(0,3), (1,6), (2,9), (3,12)$