In geometry, a linear expression typically refers to an equation that represents a line in the Cartesian plane. The general form of a linear equation is:
y = mx + b
where y is the dependent variable, x is the independent variable, m is the slope of the line, and b is the y-intercept (the point at which the line intersects the y-axis).
To graph a linear expression, you would typically plot the y-intercept (0, b) and then use the slope to find other points on the line. The slope is defined as the change in y divided by the change in x, or:
m = (y2 – y1) / (x2 – x1)
where (x1, y1) and (x2, y2) are any two points on the line.
For example, if we wanted to graph the linear expression y = 2x + 3, we would start by plotting the y-intercept at (0, 3). Then, using the slope of 2, we could find another point on the line by moving up 2 units and to the right 1 unit from the y-intercept. Plotting that point at (1, 5) and connecting the two points would give us the graph of the linear expression.