How to Graph a Linear Equation using Slope and y

Algebra 1 Tutorial

How to Graph a Linear Equation using Slope and y

Intro

Step 1: Put the equation in Slope Intercept Form

For example: y = 2x + 3 is in slope intercept form.

The number in the m position (2) is the slope and it is a positive number so the slope of the line will be a positive slope. The number in the b position (3) is the y-intercept which means this is where the graphed line will cross the y-axis.

When a linear equation is not in Slope Intercept Form, you must use your algebra skills to change it into the correct form. For example: 2y + 6 = 2x

To change the equation into slope intercept form you must first subtract 6 on both sides of the equation. By doing this, you get 2y = 2x – 6. We are almost there. We now need to isolate y on the left side of the equation. We do that by dividing both sides by 2. Remember to divide everything on the right side by 2. This gives us

y = x – 3.

Sample Problem

y = 2x + 3

Solution

Step 1: Put the equation in Slope Intercept Form

For example: y = 2x + 3 is in slope intercept form.

The number in the m position (2) is the slope and it is a positive number so the slope of the line will be a positive slope. The number in the b position (3) is the y-intercept which means this is where the graphed line will cross the y-axis.

When a linear equation is not in Slope Intercept Form, you must use your algebra skills to change it into the correct form. For example: 2y + 6 = 2x

To change the equation into slope intercept form you must first subtract 6 on both sides of the equation. By doing this, you get 2y = 2x – 6. We are almost there. We now need to isolate y on the left side of the equation. We do that by dividing both sides by 2. Remember to divide everything on the right side by 2. This gives us

y = x – 3. We now have the equation in slope intercept form and we can move on to Step 2.

Step 2: Graph the y-intercept point (the number in the b position) on the y-axis. In the example above our equation is y = x – 3 The number in the b position is a -3, so we plot a point on (0,-3) on the y axis. Sometimes you will encounter an equation that does not have a number in the b position. For example: y = 3x In this case you have a slope (3) but no y-intercept. In equations without a number in the b position, the first point is plotted at the origin (0,0).

Step 3: From the point plotted on the y-axis, use the slope to find your second point. Remember, the slope is the number in the m position in your equation. In the equation y = x – 3 the slope is 1 since the variable counts as one. The slope of a line is the slant of the line and it is expressed as \begin{aligned} \frac{rise}{run} \end{aligned} the rise being the up and down on the y-axis and the run being the distance right or left. In our example above the slope is \begin{aligned} \frac{1}{1} \end{aligned} . From the point (0,-3) on the y-axis use the slope to find the second point. In this case go up one and over one to the right to the point (1,-2). This will be your second point. Don’t get caught up in the up or down in the (rise) part of the fraction \begin{aligned} \frac{rise}{run} \end{aligned}. It’s the run, or side to side that matters since that will determine whether the line will be a positive or negative slope. In our example above, we could go down one from point (0,-3) and to the left one to maintain our positive slope.

If slope is an integer use one as denominator. If the equation is \begin{aligned} y = \frac{2}{3} \ \textrm{x} + 5 \end{aligned} the slope is already in the \begin{aligned} \frac{rise}{run} \end{aligned} form. In this example, 5 is in the b position and will be plotted as (0,5) on the y-axis. From that point you will move up 2 and over 3 to the left to the point (3,7). This will be your second and final point. Now draw your line. You will notice, that because you went up 2 and to the left 3, the line will be a negative slope.

Step 4: Draw your line using the two points you plotted (y-intercept (b) first, slope (m) second. Be sure your line is pointing the right way.



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