Understanding the Linear Equation y = 2x – 1 | Components, Graphing, and Slope

y = 2x – 1

The equation given is y = 2x – 1

The equation given is y = 2x – 1. This is a linear equation in slope-intercept form. Let’s break down the components of this equation:

– y represents the dependent variable, usually referred to as the output or the “y-coordinate” in a coordinate plane.
– x represents the independent variable, usually referred to as the input or the “x-coordinate” in a coordinate plane.
– 2 is the coefficient of x, which represents the slope of the line. The slope determines the steepness of the line and how it changes as x increases or decreases.
– -1 is the y-intercept, which is the point where the line intersects the y-axis. It represents the value of y when x is equal to zero.

To graph this equation, you can start by plotting the y-intercept, which is (0, -1). Then, you can use the slope to find additional points and connect them to form the line. The slope of 2 means that for every increase of 1 in x, y will increase by 2.

For example, if x = 1, we can substitute it into the equation to find the corresponding value of y:
y = 2(1) – 1
y = 2 – 1
y = 1
So, the point (1, 1) is on the line.

Similarly, if x = -1, we can substitute it into the equation to find y:
y = 2(-1) – 1
y = -2 – 1
y = -3
So, the point (-1, -3) is on the line.

You can continue finding more points and connecting them to form a straight line.

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