Understanding the Equation y = 2x + 2 | A Breakdown of Slope, Y-Intercept, and Graphing

y = 2x + 2

The given equation is y = 2x + 2

The given equation is y = 2x + 2.

This is an equation of a straight line in slope-intercept form, where y represents the dependent variable (the vertical axis), x represents the independent variable (the horizontal axis), 2 is the coefficient of x (the slope), and 2 is the y-intercept (the point where the line crosses the y-axis).

To understand this equation better, let’s break it down:

Slope (m): The coefficient of x in the equation represents the slope of the line. In this case, the slope is 2. This means that for every one unit increase in x, the corresponding y value will increase by 2. A positive slope indicates an upward-sloping line.

Y-intercept (b): The constant term in the equation represents the y-intercept. In this case, the y-intercept is 2. This means that the line crosses the y-axis at the point (0, 2).

Graphing the equation:
To graph this equation, start by plotting the y-intercept point (0, 2) on the graph. Then, use the slope to find the next set of points. Since the slope is 2, for each unit increase in x, the corresponding y value increases by 2. So for example, when x = 1, y = 2(1) + 2 = 4. When x = 2, y = 2(2) + 2 = 6. Plot these points on the graph and draw a straight line passing through them.

General significance:
This equation can be used to model various linear relationships, where y is determined by the value of x according to the prescribed equation. It can be used in applications such as calculating costs, predicting trends, or analyzing data points.

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