Understanding Linear Relationships | Exploring the Equation y = 4x and its Graph

y = 4x

The equation y = 4x represents a linear relationship between two variables, y and x

The equation y = 4x represents a linear relationship between two variables, y and x. In this equation, 4 is the coefficient of x, which means that for every unit increase in x, y will increase by a multiple of 4.

This equation can be graphed on a coordinate plane by plotting a series of points that satisfy the equation. To do this, you can choose different values for x and calculate the corresponding values of y. For example, when x = 0, y = 4(0) = 0. So, one point on the graph would be (0, 0). Similarly, when x = 1, y = 4(1) = 4. Another point on the graph would be (1, 4). By connecting these points and any others that you calculate, you can draw a straight line that represents the relationship between x and y.

In this case, since the coefficient of x is positive (4), the line will have a positive slope and will slope upwards from left to right. This means that as x increases, y will also increase. If the coefficient of x were negative, the slope would be negative and the line would slope downwards.

The equation y = 4x is a specific form of a linear equation called slope-intercept form (y = mx + b), where m represents the slope and b represents the y-intercept. In this case, since there is no constant term, the y-intercept is 0. This means that the line crosses the y-axis at the point (0, 0), which is the origin.

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