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Linear Equations: Understanding Slope-Intercept Form and Standard Form

Learn about linear equations, slope-intercept form, standard form, finding slopes, writing equations, and solving real-world problems with step-by-step examples and guided practice.

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Linear Equations: Understanding Slope-Intercept Form and Standard Form

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  1. 1.If 2x + 5y= –20 and x= 0, what is y? 2.What is the slope of the line containing the points (2, 7) and (3,–10)? 3.Orphelia boughtx apples. If each apple costs $.59, write an equation for y, the total cost ofx apples.

  2. Two forms of linear functions from Algebra Slope-intercept form: y = mx + b where m represents the slope and b represents the y-intercept Standard form: Ax + By = C where A, B, and C are constants.

  3. Write an equation of the line in slope- intercept form. STEP 3 Write the equation. STEP 1 Find the slope. Choose two points on the graph of the line, (0, 4) and (3, –2). Find the y-intercept. STEP 2 EXAMPLE 1 Write an equation of a line from a graph

  4. STEP 3 Plug it in! Plug it in! STEP 1 Find the slope m. STEP 2 Find the y-intercept bby using m=2 and (x, y)=(– 1, 1). EXAMPLE 2 Write an equation of a parallel line Write an equation of the line passing through the point (– 1, 1) that is parallel to the line with the equation y= 2x–3.

  5. STEP 1 Find the slope mof line j. Line khas a slope of ______. EXAMPLE 3 Write an equation of a perpendicular line Write an equation of the line jpassing through the point (2, 3) that is perpendicular to the line kwith the equation y = – 2x + 2. Find the y-intercept bby using m= _____ and (x, y)=(2, 3). STEP 2

  6. Write an equation of the line that passes through (– 2, 5) and (1, 2). Write an equation of the line that passes through the point (1, 5) and is parallel to the line with the equation y=3x–5. Graph the lines to check that they are parallel. Write an equation of the line in the graph at the right. for Examples 1, 2 and 3 GUIDED PRACTICE

  7. How do you know the lines x = 4 and y = 2 are perpendicular? for Examples 1, 2 and 3 GUIDED PRACTICE

  8. Gym Membership The graph models the total cost of joining a gym. Write an equation of the line. Explain the meaning of the slope and the y-intercept of the line. STEP 3 Write the equation. Find the slope. STEP 1 EXAMPLE 4 Write an equation of a line from a graph Find the y-intercept. Use the slope and one of the points on the graph. STEP 2

  9. Graph the line. STEP 2 STEP 1 Find the intercepts. EXAMPLE 5 Graph a line with equation in standard form Graph 3x + 4y = 12. To find the x-intercept, let y = 0. To find the y-intercept, let x= 0.

  10. The equation y = 50x + 125 models the total cost of joining a climbing gym. What are the meaning of the slope and the y-intercept of the line? 2x –3y = 6 for Examples 4 and 5 GUIDED PRACTICE Graph the equation y = 4 x = – 3

  11. STEP 2 DVD Rental Graph each equation. You can rent DVDs at a local store for $4.00 each. An Internet company offers a flat fee of $15.00 per month for as many rentals as you want. How many DVDs do you need to rent to make the online rental a better buy? STEP 1 Model each rental with an equation. EXAMPLE 6 Solve a real-world problem Cost of one month’s rental online: y = 15 Cost of one month’s rental locally: y = 4x, where xrepresents the number of DVDs rented

  12. EXAMPLE 6 Solve a real-world problem The point of intersection is (3.75, 15). Using the graph, you can see that it is cheaper to rent locally if you rent 3 or fewer DVDs per month. If you rent 4 or more DVDs per month, it is cheaper to rent online.

  13. What If?In Example 6, suppose the online rental is $16.50 per month and the local rental is $4 each. How many DVDs do you need to rent to make the online rental a better buy? How would your answer to Exercise 9 change if you had a 2-for-1 coupon that you could use once at the local store? for Example 6 GUIDED PRACTICE

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