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Algebra 1

1.5.2 Graphing Linear Functions in Two Variables

Algebra 11.5.2 Graphing Linear Functions in Two Variables

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Activity

For questions 1 - 7, use the equation 3x+4y=123x+4y=12

1.

Find the value of yy when x=0x=0.

2.

Find the value of xx when y=0y=0.

3.

Plot both of those points on a coordinate grid and use a ruler to draw a line.

4.

What is the coordinate of the xx-intercept?

5.

What is the coordinate of the yy-intercept?

6.

What are two other names for the xx-intercept?

7.

What is the slope of the line?

Self Check

Graph the equation 5x2y=105x2y=10. Which of the following describes the intercepts and slope of the graph?

  • xx-intercept: x=5x=5; yy-intercept: y=2y=2; Slope: 5252
  • xx-intercept: x=2x=2; yy-intercept: y=5y=5; Slope: 5252
  • xx-intercept: x=2x=2; yy-intercept: y=5y=5; Slope: 5252
  • xx-intercept: x=2x=2; yy-intercept: y=5y=5; Slope: 5252

Additional Resources

Graphing a Line and Describing Characteristics

There are many ways to graph an equation of a line. One way is to use the xx-intercepts and yy-intercepts as two points on the line.

Example

Graph 3x6y=183x6y=18 using the intercepts, then identify key characteristics.

Step 1 - Find the xx-intercept.
To find the xx-intercept, let y=0y=0.

3x6y=183x6(0)=183x=18x=63x6y=183x6(0)=183x=18x=6

(6,0)(6,0) is the xx-intercept
The xx-intercept is also called a solution or zero.

Step 2 -Find the yy-intercept.
To find the yy-intercept, let x=0x=0.

3x6y=183(0)6y=186y=18y=33x6y=183(0)6y=186y=18y=3

(0,3)(0,3) is the yy-intercept

Step 3 -Graph the line by connecting the yy-intercepts.

A plot of y intercepts of the equation 3x - 6y =18.

Step 4 - Find the slope of the line.

slope=riserun=36=12slope=riserun=36=12

Try it

Try It: Graphing a Line and Describing Characteristics

For 1 - 2, use the equation 7x3y=217x3y=21.

1.

Graph the equation using the intercepts.

2.

What is the slope of the line?

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