Chapter 2 Section 4. Write an equation in slope-intercept form for the line that has a slope ofand passes through (5, –2). Slope-intercept form Simplify.

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Presentation transcript:

Chapter 2 Section 4

Write an equation in slope-intercept form for the line that has a slope ofand passes through (5, –2). Slope-intercept form Simplify.

Add 3 to each side. Answer:The y -intercept is 1. So, the equation in slope-intercept form is

Write an equation in slope-intercept form for the line that has a slope ofand passes through (–3, –1). Answer:

Multiple-Choice Test Item What is an equation of the line through (2, –3) and (–3, 7) ? ABCDABCD Read the Test Item You are given the coordinates of two points on the line. Notice that the answer choices are in slope-intercept form.

Solve the Test Item First, find the slope of the line. Slope formula Simplify. The slope is –2. That eliminates choices B and C.

Then use the point-slope formula to find an equation. Point-slope form you can use either point for. Distributive Property Answer: D Subtract 3 from each side.

Answer:C Multiple-Choice Test Item What is an equation of the line through (2, 5) and (–1, 3) ? ACBDACBD

Sales As a part-time salesperson, Jean Stock is paid a daily salary plus commission. When her sales are $100, she makes $58. When her sales are $300, she makes $78. Write a linear equation to model this situation. Let x be her sales and let y be the amount of money she makes. Use the points (100, 58) and (300, 78) to make a graph to represent the situation.

Slope formula Simplify.

Now use the slope and either of the given points with the point-slope form to write the equation. Point-slope form Distributive Property Add 58 to each side. Answer:The slope-intercept form of the equation is

The y -intercept of the line is 48. The y - intercept represents the money Jean would make if she had no sales. Thus, $48 is her daily salary. Answer:Ms. Stock’s daily salary is $48, and she makes a 10% commission. What are Ms. Stock’s daily salary and commission rate? The slope of the line is 0.1. Since the slope is the coefficient of x, which is her sales, she makes 10% commission.

How much would Jean make in a day if her sales were $500? Find the value of y when Use the equation you found in Example 3a. Replace x with 500. Simplify. Answer:She would make $98 if her sales were $500.

Sales The student council is selling coupon books to raise money for the Humane Society. If the group sells 200 books, they will receive $150 dollars. If they sell 500 books, they will make $375. a.Write a linear equation to model this situation. b.Find the percentage of the proceeds that the student council receives. c.If they sold 1000 books, how much money would they receive to donate to the Humane Society? Answer: Answer: 75% Answer: $750

Write an equation for the line that passes through (3, –2) and is perpendicular to the line whose equation is The slope of the given line is –5. Since the slopes of perpendicular lines are opposite reciprocals, the slope of the perpendicular line is Use the point-slope form and the ordered pair (3, –2) to write the equation.

Point-slope form Distributive Property Subtract 2 from each side. Answer: An equation of the line is

Write an equation for the line that passes through (3, 5) and is perpendicular to the line whose equation is Answer: