The equation y equals 2x plus 1 is a linear function. It represents a straight line with a slope of 2, meaning for every unit increase in x, y increases by 2 units. The y-intercept is 1, which is where the line crosses the y-axis.
The equation y equals 2x plus 1 is written in slope-intercept form, where m represents the slope and c represents the y-intercept. The slope of 2 means that for every 1 unit we move right, we move up 2 units. This rise over run ratio gives us the steepness of the line.
To find points on the line y equals 2x plus 1, we substitute different x-values into the equation. When x is negative 1, y equals negative 1. When x is 0, y equals 1. When x is 1, y equals 3. When x is 2, y equals 5. These points all lie on our straight line.
To graph the linear function y equals 2x plus 1, we follow these steps. First, plot the y-intercept at point (0, 1). Then, use the slope of 2 to find the next point by moving right 1 unit and up 2 units from the y-intercept. This gives us the point (1, 3). Finally, draw a straight line through these points to complete the graph.
In summary, y equals 2x plus 1 is a linear function that forms a straight line. It has a slope of 2, meaning it increases by 2 units vertically for every 1 unit horizontally. The y-intercept is 1, where the line crosses the y-axis. This function is defined for all real numbers and represents a fundamental example of linear relationships in mathematics.