Understanding and Graphing the Equation y = x + 6 | Explanation of Slope and Y-Intercept

y = x + 6

The equation y = x + 6 represents a straight line on a coordinate plane

The equation y = x + 6 represents a straight line on a coordinate plane. It is in slope-intercept form, which means that the equation can be interpreted to reveal information about the slope and y-intercept of the line.

In this equation, x and y are variables representing the x-coordinate and y-coordinate of a point on the line, respectively. The number 6 is known as the y-intercept, which indicates the point where the line crosses the y-axis. In this case, the line intersects the y-axis at the point (0, 6).

The coefficient of x, which is 1 in this equation, represents the slope of the line. The slope measures the steepness of the line and determines how much y changes for a given change in x. Since the coefficient of x is positive (1), the line has a positive slope, meaning that as x increases, y also increases. In other words, the line slants upwards from left to right.

To graph this line, you would first plot the y-intercept (0, 6) on the coordinate plane. Then, you would use the slope to find additional points. For example, if you move one unit to the right (meaning x increases by 1), you would move one unit up (y increases by 1) to find the next point. Similarly, if you move two units to the right, you would move two units up, and so on. By connecting these points with a straight line, you will have graphed the equation y = x + 6.

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