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Understanding Linear Equations: Point-Slope Form and Real-World Applications**

This lesson focuses on writing linear equations using the Point-Slope Form while applying real-world scenarios. We’ll learn how to derive an equation that passes through specific points and has a given slope (e.g., (m=3) and points ((3,4)) or ((-2,2)) and ((1,8))). Additionally, we will tackle a carnival entrance and ticket pricing problem to determine costs based on provided data. Students will practice converting between linear equation forms and use these concepts in practical applications.

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Understanding Linear Equations: Point-Slope Form and Real-World Applications**

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  1. Bellwork Clickers • Write an equation that satisfies the following criteria • Passes through (3,4) and m=3 • Passes through (-2,2) & (1,8) • A carnival charges an entrance fee and a ticket fee. One person paid $27.50 and bought 5 tickets, while another paid $45 and bought 12 tickets. How much would 22 tickets cost

  2. Bellwork Solution • Write an equation that satisfies the following criteria • Passes through (3,4) and m=3

  3. Bellwork Solution • Write an equation that satisfies the following criteria • Passes through (-2,2) & (1,8)

  4. Bellwork Solution • A carnival charges an entrance fee and a ticket fee. One person paid $27.50 and bought 5 tickets, while another paid $45 and bought 12 tickets. How much would 22 tickets cost?

  5. Write Linear equations in Point-Slope Form Section 5.3

  6. The Concept • Yesterday we spent learned how to take a point and a slope to write a linear equation • Today we’re going to take a look at a another linear form, that can aid us in our efforts to write linear equations

  7. Point Slope Form • As we’ve already seen, linear equations are often just various rewritten iterations of the same equation • It make sense then that there is a form that exists that combines a point and a slope • This form is cleverly named, Point Slope Form. Today we’re going to talk about Point Slope Form • It’s common form can be seen a • This form is based on the ideas presented by slope intercept form

  8. Point Slope Form • Let’s look at how we can take this back to slope intercept form

  9. Point Slope Form • Let’s do an example involving this form • Write an equation for a line with slope 2 and passes through the point (4, -3)

  10. Point Slope Form • We can also easily convert this form back to slope-intercept form

  11. On your own • Write an equation for a line with slope 5 and passes through the point (8, -5)

  12. On your own • Write an equation for a line with slope of ½ and passes through the point (-4, 1)

  13. Practice You are designing a sticker to advertise your band. A company charges $225 for the first 1000 stickers and $80 for each additional 1000 stickers. Write an equation that gives the total cost (in dollars) of stickers as a function of the number (in thousands) of stickers ordered.

  14. Homework 5.3 Exercises 1, 2, 7-19 odd, 45-52 even

  15. Practice Example 5, page 295

  16. Most Important Points • Point-Slope Form • Changing between forms

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