Lesson Vocabulary

• x-intercept
• standard form of a linear equation

Take Note Key Concept: Standard Form of a Linear Equation

The standard form of a linear equation is A x + B y = C , eh x plus b y equals c comma  where A, B, and C are real numbers, and A and B are not both zero.

Problem 1 Finding x- and y-Intercepts

What are the x - and y-intercepts of the graph of 3 x + 4 y = 24 ? 3 bold italic x plus 4 bold italic y equals 24 question mark

• Step 1 To find the x-intercept, substitute 0 for y. Solve for x.

  3 x + 4 y = 24 3 x + 4 ( 0 ) = 24 3 x = 24 x = 8 table with 4 rows and 2 columns , row1 column 1 , 3 x plus 4 y , column 2 equals 24 , row2 column 1 , 3 x plus 4 , open 0 close , column 2 equals 24 , row3 column 1 , 3 x , column 2 equals 24 , row4 column 1 , x , column 2 equals 8 , end table

  The x-intercept is 8.

• Step 2 To find the y-intercept, substitute 0 for x. Solve for y.

  3 x + 4 y = 24 3 ( 0 ) + 4 y = 24 4 y = 24 y = 6 table with 4 rows and 2 columns , row1 column 1 , 3 x plus 4 y , column 2 equals 24 , row2 column 1 , 3 , open 0 close , plus 4 y , column 2 equals 24 , row3 column 1 , 4 y , column 2 equals 24 , row4 column 1 , y , column 2 equals 6 , end table

  The y-intercept is 6.