Question

graph the system of equations.
y = 2x + 2
y = x

Explanation:

Step1: Graph \( y = 2x + 2 \)

To graph \( y = 2x + 2 \), we can use the slope - intercept form \( y=mx + b \), where \( m \) is the slope and \( b \) is the y - intercept. For \( y = 2x+2 \), the y - intercept \( b = 2 \), so the line crosses the y - axis at \( (0,2) \). The slope \( m = 2=\frac{2}{1} \), which means from the point \( (0,2) \), we can move 1 unit to the right (increase \( x \) by 1) and 2 units up (increase \( y \) by 2) to get the next point \( (1,4) \). We can also find the x - intercept by setting \( y = 0 \): \( 0=2x + 2\Rightarrow2x=-2\Rightarrow x=-1 \), so the line also passes through \( (-1,0) \).

Step2: Graph \( y=x \)

For the equation \( y = x \), it is also in slope - intercept form \( y=mx + b \) with \( m = 1 \) and \( b = 0 \). The y - intercept is \( (0,0) \). The slope \( m = 1=\frac{1}{1} \), so from the point \( (0,0) \), we can move 1 unit to the right and 1 unit up to get the point \( (1,1) \), or 1 unit to the left and 1 unit down to get the point \( (-1,-1) \).

Answer:

To graph the system:

• For \( y = 2x+2 \): Plot the points \( (0,2) \), \( (1,4) \), \( (-1,0) \) and draw a straight line through them.
• For \( y = x \): Plot the points \( (0,0) \), \( (1,1) \), \( (-1,-1) \) and draw a straight line through them. The two lines will intersect at the solution of the system (which can be found by solving \( 2x + 2=x\Rightarrow x=-2,y = - 2 \), but for graphing, we just need to plot the lines as described).