Question

graphing linear equations
vectored instruction
graph the equation by filling in the chart.
equation: y = 2x - 1
(graph with x-axis from -3 to 6, y-axis from -3 to 10, points at (0, -1) and (1, 1) plotted)
x | y
0 | -1
1 | 1
2 | ?
3 |
4 |

Explanation:

Step1: Substitute x = 2 into the equation

We have the equation \( y = 2x - 1 \). When \( x = 2 \), we substitute \( x \) with 2 in the equation.
\( y = 2\times2 - 1 \)

Step2: Calculate the value of y

First, calculate \( 2\times2 = 4 \), then subtract 1 from 4.
\( y = 4 - 1 = 3 \)

Step3: Substitute x = 3 into the equation

When \( x = 3 \), substitute \( x \) with 3 in \( y = 2x - 1 \).
\( y = 2\times3 - 1 \)

Step4: Calculate the value of y for x = 3

First, \( 2\times3 = 6 \), then subtract 1 from 6.
\( y = 6 - 1 = 5 \)

Step5: Substitute x = 4 into the equation

When \( x = 4 \), substitute \( x \) with 4 in \( y = 2x - 1 \).
\( y = 2\times4 - 1 \)

Step6: Calculate the value of y for x = 4

First, \( 2\times4 = 8 \), then subtract 1 from 8.
\( y = 8 - 1 = 7 \)

Answer:

For \( x = 2 \), \( y = 3 \); for \( x = 3 \), \( y = 5 \); for \( x = 4 \), \( y = 7 \)

Filling the table:

x	y
1	1
2	3
3	5
4	7