bell quiz. objectives learn to find the x- and y-intercepts of a linear equation algebraically....

Bell Quiz

Objectives

• Learn to find the x- and y-intercepts of a linear equation algebraically.

• Locate x- and y-intercepts on a graph, and use them to graph a liner equation.

Linear Equations

• Linear equations can be graphed by making a table of ordered pairs that satisfy the equation and then graphing the corresponding points (x, y).

• An ordered pair or set of ordered pairs that satisfy an equation is called the solution of a linear equation in two variables.

• When an equation is in standard form, the linear equation can be graphed another way.

Standard Form of a Linear Equation

• The Standard form of a linear equation is:

Ax + By = C

– Where A, B, and C are real numbers and A and B are not both zero

Standard Form

• The x-coordinate of the point where the graph of an equation intersects the x-axis is called the x-intercept.

• The y-coordinate of the point where the graph of an equation intersects the y-axis is called the y-intercept.

• The coordinate pairs (x, 0) and (0, y) that satisfy a linear equation are two solutions of the linear equation in two variables.

Example 1Finding x- and y-Intercepts

Find the x- and y-intercepts

3x + 4y = 24

Lesson Practice

Find the x- and y-intercepts

–6x + 9y = 36

Graphing

• An efficient method for graphing a linear equation in two variables is to: – plot the x- and y-intercepts.– Then draw a line through them.

Example 2Graphing Using the x- and y-Intercepts

Graph using the x- and y-intercepts

5x – 6y = 30

Lesson Practice

Graph using the x- and y-intercepts

4x + 7y = 28

Example 3Locating x- and y- intercepts on a Graph

Find the x- and y-intercepts on the graph.

Lesson Practice

Find the x- and y-intercepts on the graph.

Standard Form

• Any linear equation can be rearranged into standard form.

• Put both variables and their coefficients on one side of the equal sign and the constants on the other side.

Example 4Using Standard Form to Graph

Write the equation in standard form, then graph.

y = – + 5

Lesson Practice

Write the equation in standard form, then graph.

4y = 12x – 12

Example 5Application: Play Tickets

At the school play, students tickets are $5 and adult tickets are $8. Let x be the number of student tickets sold. Let y be the number of adult tickets sold. The equation 5x + 8y = 400 shows that one drama club member raised $400 from ticket sales. Find the intercepts and explain what each means.

Lesson Practice

Harvey jogs 6 miles per hour and bikes 12 miles per hour. The equation 6x + 12y = 24 shows that he has gone a total of 24 miles. Find the intercepts and explain what each means.