Writing Equations in Slope-Intercept Form Online Graphing Calculator

Example 4-1a 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 the slope-intercept form. Then, solve for b. Write an Equation Given Slope and One Point

Example 4-1b 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 4-1c Step 2Write the slope-intercept form using Slope-intercept form Replace m with and b with –4. Answer:The equation is Write an Equation Given Slope and One Point You can check your results using a graphing calculator! Online Graphing Calculator

Example 4-1e Write an equation of a line that passes through (1, 4) and has a slope of –3. Answer: Write an Equation Given Slope and One Point 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.

Example 4-2a 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? AB CD xy –3–4 –2–8 Read the Test Item The table represents the ordered pairs (–3, –4) and (–2, –8). Write an Equation Given Two Points

Example 4-2b Solve the Test Item Step 1Find the slope of the line containing the points. Let and. Slope formula 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). 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 4-2d Step 3Write the slope-intercept form using Answer:The equation isThe answer is D. Slope-intercept form Replace m with –4 and b with –16. Write an Equation Given Two Points

Example 4-2e xy –13 26 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? AB CD Answer:B Write an Equation Given Two Points

Writing Equations in Slope-Intercept Form You may need to rewrite the information as two points then find the slope and y-intercept.

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 and June. PlanLet x represent the month and y represent the cost of gasoline that month. Write an equation of the line that passes through (5, 1.76) and (6, 2.13). Write an Equation to Solve a Problem

Example 4-3b SolveFind the slope. Let and. Slope formula Simplify. Write an Equation to Solve a Problem

Example 4-3c Choose (5, 1.76) and find the y-intercept of the line. Slope-intercept form Replace m with 0.37, x with 5, and y with Multiply. Subtract 1.85 from each side. Simplify. Write an Equation to Solve a Problem

Example 4-3d Slope-intercept form Write the slope-intercept form using and Replace m with 0.37 and b with –0.09. Answer:The equation is Write an Equation to Solve a Problem

Example 4-3e ExamineCheck your result by substituting the coordinates of the point not chosen, (6, 2.13), into the equation. Original equation Replace y with 2.13 and x with 6. Multiply. Simplify. Write an Equation to Solve a Problem

Example 4-3f The average cost of a college textbook in 1997 was $ In 2000, the average cost was $ Write a linear equation to estimate the average cost of a textbook in any given year since Let x represent years since Answer: Write an Equation to Solve a Problem

Writing Equations in Slope-Intercept Form

Linear extrapolation is 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.

Example 4-4a 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 to add to their budget. Explain. Original equation Replace x with 7. Simplify. Linear Extrapolation Answer:If gas increases at the same rate, a gallon of gasoline will cost $2.50 in July gallons at this price is $7500, so they will have to add $500 to their budget.

Example 4-4c A student is starting college in 2004 and has saved $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 determine whether they will have enough money for 5 textbooks. Answer:If the cost of textbooks increases at the same rate, the average cost will be $82.15 in Five textbooks at this price is $410.75, so he will not have enough money. Linear Extrapolation