Question

graph the equation ( y = x + 5 ). let ( x = -3, -2, -1, 0, 1, 2, ) and ( 3 ).
find the ( y )-values for the following points on the graph of the equation.

( x )	( y )
( -2 )	( 3 )
( -1 )	( 4 )
( 0 )	( 5 )
( 1 )	( 6 )
( 2 )	( 7 )
( 3 )	( 8 )

choose the correct graph of the equation
\\( \bigcirc \\) a.
\\( \bigcirc \\) b.
\\( \bigcirc \\) c.
\\( \bigcirc \\) d.

Explanation:

Step1: Analyze the equation's properties

The equation $y = x + 5$ is a linear function with a slope $m=1$ (positive, so the line rises from left to right) and y-intercept $b=5$ (the line crosses the y-axis at $(0,5)$).

Step2: Verify given points

For each $x$ value:

• When $x=-3$, $y=-3+5=2$
• When $x=-2$, $y=-2+5=3$
• When $x=-1$, $y=-1+5=4$
• When $x=0$, $y=0+5=5$
• When $x=1$, $y=1+5=6$
• When $x=2$, $y=2+5=7$
• When $x=3$, $y=3+5=8$

These points all lie on a line with positive slope passing through $(0,5)$.

Step3: Match to the correct graph

Compare with options:

• A: Line has positive slope but does not pass through $(0,5)$
• B: Line has negative slope, incorrect
• C: Line has negative slope, incorrect
• D: Line has positive slope and passes through $(0,5)$, matching the points and equation.

Answer:

D. <The graph with positive slope passing through (0,5) and the given points>