Understanding Linear Functions | Exploring the Equation y = 3/4 x – 2 and Plotting the Graph

y = 3/4 x – 2

The equation y = 3/4 x – 2 represents a linear function

The equation y = 3/4 x – 2 represents a linear function. Let’s break it down:

The equation follows the form of a linear equation: y = mx + b. In this case, m represents the slope of the line, and b represents the y-intercept.

In the given equation, the slope (m) is 3/4. This means that for every unit increase in x, y will increase by 3/4. The positive slope indicates that the line will be upward sloping.

The y-intercept (b) is -2, which means that the line intersects the y-axis at the point (0, -2). It is the value of y when x is equal to 0.

Using this information, you can plot the graph of this equation by starting at the y-intercept (-2) and then using the slope (3/4) to find additional points. To find other points, you can choose different x-values, substitute them into the equation, and then calculate the corresponding y-values.

For example, when x = 4, you can substitute it into the equation:
y = 3/4 * 4 – 2
y = 3 – 2
y = 1

So, another point on the line is (4, 1).

By continuing this process, you can find as many points as needed to plot the line accurately.

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