Graph Linear Equations Worksheet

Understanding Linear Equations

Linear equations are equations in which the highest power of the variable(s) is 1. They are called linear because the graph of a linear equation is a straight line. In this post, we will explore how to graph linear equations and provide a worksheet for practice.

Forms of Linear Equations

There are three main forms of linear equations:

• Slope-Intercept Form: y = mx + b, where m is the slope and b is the y-intercept.
• Standard Form: Ax + By = C, where A, B, and C are constants.
• Point-Slope Form: y - y1 = m(x - x1), where m is the slope and (x1, y1) is a point on the line.

Graphing Linear Equations

To graph a linear equation, you can use the following steps:

1. Identify the form of the equation. If it’s not in slope-intercept form, rewrite it.
2. Determine the slope (m) and y-intercept (b).
3. Plot the y-intercept on the graph.
4. Use the slope to find another point on the line.
5. Draw a straight line through the two points.

Example 1: Graphing a Linear Equation in Slope-Intercept Form

Suppose we want to graph the equation y = 2x + 3.

1. The equation is already in slope-intercept form.
2. The slope is 2, and the y-intercept is 3.
3. Plot the point (0, 3) on the graph.
4. Use the slope to find another point on the line. For example, if x = 1, then y = 2(1) + 3 = 5. So, plot the point (1, 5).
5. Draw a straight line through the two points.

📝 Note: You can also use a table of values to graph a linear equation. Simply plug in different values for x and calculate the corresponding y-values.

Example 2: Graphing a Linear Equation in Standard Form

Suppose we want to graph the equation 2x + 3y = 6.

1. Rewrite the equation in slope-intercept form. Subtract 2x from both sides to get 3y = -2x + 6. Then, divide both sides by 3 to get y = (-²⁄₃)x + 2.
2. The slope is -²⁄₃, and the y-intercept is 2.
3. Plot the point (0, 2) on the graph.
4. Use the slope to find another point on the line. For example, if x = 1, then y = (-²⁄₃)(1) + 2 = ⁴⁄₃. So, plot the point (1, ⁴⁄₃).
5. Draw a straight line through the two points.

Worksheet: Graphing Linear Equations

Graph the following linear equations:

1. y = 3x - 2
2. 2x + 5y = 10
3. y - 2 = -4(x - 1)
4. x + 2y = 7
5. y = (¹⁄₂)x + 3

📝 Note: Use the steps outlined above to graph each equation.

Answer Key

1. y = 3x - 2: slope = 3, y-intercept = -2
2. 2x + 5y = 10: slope = -²⁄₅, y-intercept = 2
3. y - 2 = -4(x - 1): slope = -4, y-intercept = 6
4. x + 2y = 7: slope = -¹⁄₂, y-intercept = ⁷⁄₂
5. y = (¹⁄₂)x + 3: slope = ¹⁄₂, y-intercept = 3

By following these steps and practicing with the worksheet, you should be able to graph linear equations with ease. Remember to identify the form of the equation, determine the slope and y-intercept, and use the slope to find another point on the line.