Download
1 / 22
220 likes | 620 Views
Writing Equations in Slope-Intercept Form. Writing Equations in Slope-Intercept Form. Online Graphing Calculator. Write an equation of a line that passes through (2 , –3) with slope .
E N D
Writing Equations in Slope-Intercept Form Writing Equations in Slope-Intercept Form Online Graphing Calculator
Write an equation of a line that passes through (2, –3)with slope Step 1The line has slope To find the y-intercept,replace m with and (x, y) with (2, –3) in theslope-intercept form. Then, solve for b. Example 4-1a Write an Equation Given Slope and One Point
Slope-intercept form Replace m with ,y with –3,and x with 2. Multiply. Subtract 1 from each side. Simplify. Write an Equation Given Slope and One Point Example 4-1b
Step 2Write the slope-intercept form using Slope-intercept form Replace m with and b with –4. Answer: The equation is Example 4-1c Write an Equation Given Slope and One Point You can check your results using a graphing calculator! Online Graphing Calculator
Answer: Example 4-1e Write an Equation Given Slope and One Point Write an equation of a line that passes through (1, 4)and has a slope of –3. You can check your results using a graphing calculator! Online Graphing Calculator
Writing Equations in Slope-Intercept Form If you are not given the slope but you know two points on the line, find the slope first then choose one of the points to find the y-intercept. Writing Equations in Slope-Intercept Form
Multiple-Choice Test Item The table of ordered pairs shows the coordinates of two points on the graph of a function. Which equation describes the function? A B C D Write an Equation Given Two Points Example 4-2a Read the Test Item The table represents the ordered pairs (–3, –4)and (–2, –8).
Step 1Find the slope of the line containing the points.Let and . Slope formula Simplify. Write an Equation Given Two Points Example 4-2b Solve the Test Item
Slope-intercept form Replace m with –4,x with –3, and y with –4. Multiply. Subtract 12 from each side. Simplify. Write an Equation Given Two Points Example 4-2c Step 2You know the slope and two points. Choose one point and find the y-intercept.In this case, we chose (–3, –4).
Step 3Write the slope-intercept form using Slope-intercept form Replace m with –4 and b with –16. Answer: The equation is The answer is D. Write an Equation Given Two Points Example 4-2d
Multiple-Choice Test Item The table of ordered pairs shows the coordinates of two points on the graph of a function. Which equation describes the function? A B C D Write an Equation Given Two Points Example 4-2e Answer: B
Writing Equations in Slope-Intercept Form You may need to rewrite the information as two points then find the slope and y-intercept. Writing Equations in Slope-Intercept Form
Write an Equation to Solve a Problem Example 4-3a Economy In 2000, the cost of many items increased because of the increase in the cost of petroleum. In Chicago, a gallon of self-serve regular gasoline cost $1.76 in May and $2.13 in June. Write a linear equation to predict the cost of gasoline in any month in 2000, using 1 to represent January. Explore You know the cost of regular gasoline in May andJune. Plan Let x represent the month and yrepresent the cost of gasoline that month.Write an equation of the line that passes through (5, 1.76) and(6, 2.13).
Slope formula Letand . Simplify. Write an Equation to Solve a Problem Example 4-3b Solve Find the slope.
Slope-intercept form Replace m with0.37, x with 5,and y with 1.76. Multiply. Subtract 1.85 from each side. Simplify. Write an Equation to Solve a Problem Example 4-3c Choose (5, 1.76) and find the y-intercept of the line.
Write the slope-intercept form usingand Slope-intercept form Replace m with 0.37 and b with –0.09. Answer: The equation is Write an Equation to Solve a Problem Example 4-3d
Original equation Replace y with 2.13 and x with 6. Multiply. Simplify. Write an Equation to Solve a Problem Example 4-3e Examine Check your result by substituting the coordinates of the point not chosen, (6, 2.13), into theequation.
Answer: Write an Equation to Solve a Problem Example 4-3f Theaverage cost of a college textbook in 1997 was $57.65.In 2000, the average cost was $68.15. Write a linearequation to estimate the average cost of a textbook in any given year since 1997. Let x represent years since1997.
Writing Equations in Slope-Intercept Form Writing Equations in Slope-Intercept Form Copy all of this in your notes, PLEASE!
Writing Equations in Slope-Intercept Form Linear extrapolationis when you use a linear equation to predict values that are beyond the range of the data. Be cautious when making a prediction using just two given points. The model may be approximately correct but still give inaccurate predictions. Writing Equations in Slope-Intercept Form
Economy The Yellow Cab Company budgeted $7000 for the July gasoline supply.On average, they use 3000 gallons of gasoline per month.Use the prediction equation where x represents the month and y represents the cost of one gallon of gasoline, to determine if they will have toadd to their budget.Explain. Original equation Replace x with 7. Simplify. Linear Extrapolation Example 4-4a Answer: If gas increases at the same rate, a gallon of gasoline will cost $2.50 in July. 3000 gallons at this price is $7500, so they will have to add $500 to their budget.
A student is starting college in 2004 and hassaved$400 to use for textbooks.Use the prediction equation where x is the years since 1997 and y is the average cost of a college textbook, to determinewhether they will have enough money for 5textbooks. Linear Extrapolation Example 4-4c Answer: If the cost of textbooks increases at the same rate, the average cost will be $82.15 in 2004. Five textbooks at this price is $410.75, so he will not have enough money.
