In the formula, you will be solving for (x,y). The variable m= slope. The slope is also noted as rise over run, or the number of points you travel up and over. In the formula, b= y-intercept. This is the place on your graph where the line will cross over the y-axis.
The y-intercept is always graphed with x=0. Therefore, the y-intercept coordinates are (0,-1). Place a point on your graph where the y-intercept should be.
To graph the slope, begin at the y-intercept. The rise (number of spaces up) is the numerator of the fraction, while the run (number of spaces to the side) is the denominator of the fraction. In our example, we would graph the slope by beginning at -1, and then moving up 2 and to the right 1. A positive rise means that you will move up the y-axis, while a negative rise means you will move down. A positive run means you will move to the right of the x-axis, while a negative run means you will move to the left of the x-axis. You can mark as many coordinates using the slope as you would like, but you must mark at least one.
If you are given a “greater than” symbol, which is either > or <, then draw an open circle around the number. If you are given a “greater than or equal to” symbol, either > or <, then fill in the circle around your point.
Slope intercept form is y=mx+b, where m=slope and b=y-intercept. Having an inequality present means that there are multiple solutions.
Choose a coordinate - the origin at (0,0) is often the easiest. Make sure that you note if this coordinate is above or below the line you’ve drawn. Substitute these coordinates into your inequality. Following our example, it would be 0>1/2(0)+1. Solve this inequality. If the coordinate pair is a point above your line and the answer is true, then you would shade above the line. If the answer to the inequality is false, then you would shade below the line. If the coordinate lies below your line and the answer is true, then you shade below your line. If your answer is false, then shade above our line. In our example, (0,0) is below our line and creates a false solution when substituted into the inequality. That means that we shade the remainder of the graph above the line. [12] X Research source
Graphing a quadratic equation will give you a parabola, which is a ‘U’ shaped curve. You will need to find at least three point to graph it, beginning with the vertex which is the centermost point.
Place the x-coordinate for the vertex in the top center column. Choose two more x-coordinates an equal number in each direction (positive and negative) from the vertex point. For example, we could go up two and down two, making the two numbers we fill in the other blank table spaces ‘-3’ and ‘1’. You can choose any numbers you want to fill in the top row of the table, as long as they are whole numbers and the same distance from the vertex. If you want to have a clearer graph, you can find five coordinates instead of three. Doing this is the same process as above, but give your table five columns instead of three.
Following our example, we could use our chosen coordinate of ‘-3’ to substitute into the original formula of y=x(squared)+2x+1. This would change to y= -3(squared)+2(3)+1, giving an answer of y=4. Place the new y-coordinate underneath the x-coordinate that you used into your table. Solve for all three (or five, if you want more) coordinates in this fashion.
If your inequality symbol was “greater than” or “less than” (> or <), then you will draw a dashed line between the coordinates. If your inequality symbol was “greater than or equal to” or “less than or equal to” (> or <), then the line you draw will be solid. End your lines with arrow points to show that the solutions extend beyond the range of your graph.
Solve the inequality with the coordinates you’ve chosen. If we use an example of y>x(squared)-4x-1 and substitute the coordinates (0,0), then it will change to 0>0(squared)-4(0)-1. If the solution to this is true and the coordinates are inside the parabola, shade inside the parabola. If the solution is false, shade outside of the parabola. If the solution to this is true and the coordinates are outside the parabola, shade the outside of the parabola. If the solution is false, shade inside the parabola. [21] X Research source
The absolute value is the number of points from |x| to ‘0’ on a number line. So the absolute value of |2| is 2, and the absolute value of |-2| is also two. This is because in both cases, ‘2’ and ‘-2’ are 2 steps away from zero on the number line. You may have an absolute value equation where ‘x’ is alone. In that case, the absolute value is ‘0’. For example, y=|x|+3 changes to y=|0|+3, which equals to ‘3’.
Put the first absolute value coordinate in the into the top center column for ‘X’. Choose two other numbers an equal distance from your x-coordinate in each direction (positive and negative). If |x|=0, then move up and down an equal number of spaces from ‘0’. You can choose any numbers, although ones that are near the x-coordinate are most helpful. They must also be whole numbers.
