Questions: Complete the table below for the equation (y=5x+6). Then use two of the ordered pairs to graph the equation. y=5x+6

Transcript text: Complete the table below for the equation $y=5 x+6$. Then use two of the ordered pairs to graph the equation. \[ y=5 x+6 \]

Solution

Solution Steps

Step 1: Calculate y-values for each x-value

Substitute each given x-value into the equation y = 5x + 6:

x = -2: y = 5(-2) + 6 = -10 + 6 = -4
x = -1: y = 5(-1) + 6 = -5 + 6 = 1
x = 0: y = 5(0) + 6 = 0 + 6 = 6
x = 1: y = 5(1) + 6 = 5 + 6 = 11
x = 2: y = 5(2) + 6 = 10 + 6 = 16

Step 2: Form Ordered Pairs

The ordered pairs are (x, y):

(-2, -4)
(-1, 1)
(0, 6)
(1, 11)
(2, 16)

Step 3: Plot two points and draw the line

Plot any two of the ordered pairs calculated above on the graph. For example, plot (-2, -4) and (0, 6). Then draw a straight line through those two points. This line represents the graph of the equation y = 5x + 6.

Final Answer

| x | y | Ordered Pair | |---|---|---| | -2 | -4 | (-2, -4) | | -1 | 1 | (-1, 1) | | 0 | 6 | (0, 6) | | 1 | 11 | (1, 11) | | 2 | 16 | (2, 16) |

The graph is a straight line passing through the points calculated above. (A sketch showing the line passing through at least two of the calculated points would ideally be included here.)

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