Question

what is the graph of the equation 2×-y=2

Answer 1

[AI-generated answer — Bot GPT 3.5]

To graph the equation 2x - y = 2, we can rearrange the equation to the slope-intercept form y = mx + b.

Start by isolating y:
2x - y = 2
-y = -2x + 2
y = 2x - 2

Now we can identify the slope (m) and the y-intercept (b).
The slope (m) is 2, meaning that for every unit increase in x, y increases by 2.
The y-intercept (b) is -2, meaning that the line crosses the y-axis at y = -2.

Plot the y-intercept at (0, -2), and then use the slope to find additional points.
For example, starting from the y-intercept, move 1 unit to the right (increase x by 1) and move 2 units upward (increase y by 2). This gives a point (1, 0).

With these two points plotted, draw a straight line through them to represent the equation.

The graph of the equation 2x - y = 2 is a straight line that passes through the points (0, -2) and (1, 0).

Answer 2

[AI-generated answer — Explain Bot]

To find the graph of the equation 2x - y = 2, we can use a method known as slope-intercept form. The equation can be rewritten as y = 2x - 2.

In slope-intercept form, the equation represents a straight line, where the coefficient of x is the slope (m) of the line, and the constant is the y-intercept (b), which is the point where the line intersects the y-axis.

By comparing the equation y = 2x - 2 to the slope-intercept form y = mx + b, we can identify that the slope (m) is 2, and the y-intercept (b) is -2.

To graph this line, we can start by plotting the y-intercept at the point (0, -2), which is the point where the line crosses the y-axis. This will serve as our starting point.

From there, we can use the slope, which is 2, to find additional points. The slope tells us that for every unit we move to the right along the x-axis, the line moves up by 2 units.

So, starting at the y-intercept (0, -2), we can move one unit to the right and two units up to find the next point. This gives us the point (1, 0).

We can repeat this process to find more points if needed, always moving one unit to the right and two units up.

Once we have several points, we can connect them with a straight line. The resulting line represents the graph of the equation 2x - y = 2.

Note that since the coefficient of x is positive (2), the line slants upward from the left to the right.

Answer 3

[AI-generated answer — Step-by-Step Bot]

To graph the equation 2x - y = 2, we can rearrange it into slope-intercept form (y = mx + b), where m is the slope and b is the y-intercept.

Starting with the given equation:
2x - y = 2

First, let's isolate y on one side of the equation:
-y = -2x + 2

Next, isolate y by multiplying every term by -1:
y = 2x - 2

Now we have the equation in slope-intercept form, where the slope (m) is 2 and the y-intercept (b) is -2.

To plot the graph, we need at least two points.

1. Let's substitute x = 0 into the equation:
y = 2(0) - 2
y = -2

So, one point on the graph is (0, -2).

2. Let's substitute x = 1 into the equation:
y = 2(1) - 2
y = 0

Another point on the graph is (1, 0).

With these two points, we can now plot the graph.