## y = 2x + 2

### What is the rule for the function?

The equation y = 2x + 2 is in slope-intercept form, where the coefficient of x is the slope, and the constant at the end is the y-intercept.

– Slope: Since the coefficient of x is 2, the slope of this line is 2. This means that for every one unit increase in x, the value of y increases by 2 units. If the slope were negative, then the line would be decreasing as x increases.

– Y-intercept: The constant term in the equation is 2, which means that the line crosses the y-axis at the point (0, 2). This is the y-intercept, which is the point where x = 0.

Graphically, the line represented by y = 2x + 2 is a straight line that passes through the point (0, 2) and has a slope of 2. You could plot points on the line by picking any value for x, plugging that value into the equation, and solving for y. Some common points to plot are:

– When x = 0, y = 2. So the point (0, 2) is on the line.

– When x = 1, y = 4. So the point (1, 4) is on the line.

– When x = -1, y = 0. So the point (-1, 0) is on the line.

You can plot more points if desired, but these three points are enough to give a good idea of what the line looks like.

Lastly, it’s worth noting that if you wanted to find the x-intercept of this line (the point where the line crosses the x-axis), you would set y to zero and solve for x:

0 = 2x + 2

-2 = 2x

-1 = x

So the x-intercept is (-1, 0).

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