Warm Up Solutions

Write the equation or inequality of the line in slope-intercept form.

$y = - \frac{1}{3} x + 2$

Note

Q: How do you determine the slope from a graph?
A: Pick two points on grid lines. Then find rise (up/down) over run (left/right), or change in y over change in x.

$y \leq \frac{1}{4} x - 2$

Note

Q: How can you determine the direction of the inequality symbol for this problem?
A: Sample: You can use a test point to determine if the shaded region is being represented by substituting an ordered pair into the inequality to check that it is a true statement.

Q: Explain if (0, –2) is a solution to your inequality.
A: The ordered pair is a solution because points on a solid line make the inequality true.

You may also use technology and try different symbols until your graph matches the given graph. Checking an equation or inequality using technology will be useful throughout this level. (Algebra 1: Principles of Secondary Mathematics, or Algebra 1: PSM, Unit 2)

On the coordinate plane for problem 1, add the graph of the equation: $y = \frac{4}{3} x - 3$
Equation is graphed on the coordinate plane from problem 1.

Name the solution to the system created from problems 1 and 3.
(3, 1)

Note

Q: Why is it important to be accurate when graphing a system?
A: Sample: Being accurate is important because you need to be able to find the intersection point, which is the solution.

Systems of equations can be solved by graphing, substitution, or elimination. See Algebra 1: Principles of Mathematics.