Understanding Linear Functions | The Equation y = 5x and Its Components

y = 5x

The equation y = 5x represents a linear function where the value of y is determined by multiplying the value of x by 5

The equation y = 5x represents a linear function where the value of y is determined by multiplying the value of x by 5. In other words, for every value of x, the corresponding value of y is five times that value of x.

Here are a few important definitions related to this equation:

1. Linear Function: A linear function is a mathematical relationship between two variables, x and y, where the equation that represents the function forms a straight line when graphed. The equation for a linear function is typically written as y = mx + b, where m is the slope of the line and b is the y-intercept.

2. Slope: The slope of a line represents the steepness or slant of the line. In the equation y = 5x, the slope is 5. It indicates that for every unit increase in x, y increases by 5.

3. y-intercept: The y-intercept is the point at which the graph of a linear function intersects the y-axis. In the equation y = 5x, the y-intercept is 0 because the line passes through the origin (0, 0).

4. Graphing the Equation: To graph the equation y = 5x, you can choose a set of x-values, substitute them into the equation to find the corresponding y-values, and then plot the points on a coordinate plane. Since the equation is linear, you only need to plot two points to determine the line. In this case, the points (0, 0) and (1, 5) would be sufficient.

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