How to graph linear equations?

  1. Determine the equation: The standard form of a linear equation is y = mx + b, where m is the slope and b is the y-intercept.

  2. Identify the slope: The slope (m) is the coefficient of x in the equation. If the equation is not in standard form, rearrange it so that it is in standard form, y = mx + b.

  3. Identify the y-intercept: The y-intercept (b) is the value of y when x is zero. It is the constant in the equation.

  4. Plot the y-intercept: Plot the point (0, b) on the coordinate plane. This is the starting point for your graph.

  5. Use the slope to plot additional points: From the y-intercept point, use the slope to find additional points on the line. To do this, use the formula: m = (y2 – y1) / (x2 – x1), where (x1, y1) is the y-intercept point and (x2, y2) is any other point on the line. Once you have found a second point, you can draw a line through the two points to create the graph.

  6. Check your work: Once you have graphed the line, check your work to make sure it looks correct. The line should be straight and go through both plotted points.

Here is an example:

Graph the equation y = 2x + 1.

  1. Determine the equation: The equation is y = 2x + 1.

  2. Identify the slope: The slope is 2.

  3. Identify the y-intercept: The y-intercept is 1.

  4. Plot the y-intercept: Plot the point (0, 1) on the coordinate plane.

  5. Use the slope to plot additional points: To find another point, we can use (1, 3), since if we plug in x=1 we get y=3, which is 2 units above the y-intercept.

  6. Check your work: Once we have plotted both points (0, 1) and (1, 3), we can draw a straight line through them to create the graph. The graph of y = 2x + 1 is a straight line with a slope of 2 and a y-intercept of 1.