Understanding Linear Equations | Exploring the Equation y = 2x – 1 and its Graph

y = 2x – 1

The equation y = 2x – 1 represents a linear equation in slope-intercept form

The equation y = 2x – 1 represents a linear equation in slope-intercept form. In this form, “y” represents the dependent variable (the output) and “x” represents the independent variable (the input).

Here’s a breakdown of the equation:

– The coefficient of “x” is 2, which represents the slope of the line. This means that for every increase of 1 in the value of “x”, the value of “y” will increase by 2. Similarly, for every decrease of 1 in “x”, “y” will decrease by 2. The slope of 2 indicates that the line has a positive, upward slope.
– The constant term -1 is the y-intercept, which is the point where the line intersects the y-axis. In this case, the y-intercept is -1, meaning that the line crosses the y-axis at the point (0, -1).

You can also use this equation to find specific points on the line. For example, if you substitute x = 0 into the equation, you’ll find the y-coordinate of the y-intercept:
y = 2(0) – 1
y = -1

Similarly, you can substitute different x-values to find other points on the line. For instance, substituting x = 1 would give us:
y = 2(1) – 1
y = 1

So we have another point on the line: (1, 1).

By plotting these individual points and connecting them with a straight line, you will be able to graph the equation y = 2x – 1 and visualize the relationship between “x” and “y”.

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