Warm-Up 1. What is the slope & y-intercept of the line 2x – 5y = 10? 2. Find the slope between the points (-15, -3) and (6, 4) 3. Write the equation of.

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Presentation transcript:

Warm-Up 1. What is the slope & y-intercept of the line 2x – 5y = 10? 2. Find the slope between the points (-15, -3) and (6, 4) 3. Write the equation of the line in slope-intercept form.

HW Check 4B.2 33. 5x + 10y = 200 34. 5x + 3y = 450 35. 5x + 7y = 70 21. 4x - y = 11 22. 2x - y = 6 23. 2x + y = -3 25. 2x - 3y = 25 27. 4x + 5y = 6 28. x + 5y = 0 29. 5x - 2y = 44 33. 5x + 10y = 200 34. 5x + 3y = 450 35. 5x + 7y = 70

Standard Form Only write equations in standard form if you are given a word problem. Only write a word problem in standard form if you are NOT given a rate and a flat fee. Standard form word problems can only be written if you have two unknowns that add up to a total. DO NOT write an equation in standard form if you are given the slope and y-intercept. That equation should be written in _____________ form.

Quick Review 1. What is the Slope-Intercept Form? y = mx + b 2. What is the Standard Form? Ax + By = C 3. How does an equation of a vertical line look? What is the slope? x = #, slope = undefined 4. How does an equation of a horizontal line look? What is the slope? y = #, slope = 0

Point-Slope Form m = slope y – y1 = m(x – x1) m = slope (x1,y1) = a point that the line goes through Best used when: When you are given the slope and a point (that is not the y-intercept) and you need to write the equation of the line.

Goes through point (5, 6) and has slope of 3 Point – Slope Form y – y1 = m(x - x1) SLOPE y – coordinate x – coordinate Write the equation in point-slope form that Goes through point (5, 6) and has slope of 3 Example: y – 6 = 3(x – 5)

Point-Slope Form 1. Write the equation in Point-Slope Form of the graph below if it goes through the point (-5,-4) and has a slope of 2/3: (x, y)

Write an Equation in Point-Slope Form Given a Point and a Slope y + 3 = 4(x + 1) 3. (-10, 0); Slope = 2 y = 2(x +10) 4. (-4, 3); Slope = -6 y – 3 = -6(x +4)

Write an Equation in Point-Slope Form Given Two Points Steps: Find the slope between the two points. Pick one point to use in order to write the equation. Plug in the slope and coordinate from the point into the Point-Slope Form

Write an Equation in Point-Slope Form Given Two Points 5. (-3, 6) and (1, -2) y – 6 = -2(x + 3) or y + 2 = -2(x – 1) 6. (-2, 3) and (-1, 1) y – 3 = -2(x + 2) or y – 1 = -2(x + 1) 7. (-2, -5) and (7, -6) y + 5 = - (x + 2) or y + 6 = - (x – 7)

Writing an Equation from a Table What is the independent and dependent variable? x – independent; y – dependent Find the rate of change: What is the slope? 4/10 = 2/5 What is one ordered pair? (-11, -7), (-1, -3), (4, -1), (19, 5) What is a possible equation in Point-Slope Form? y + 7 = 2/5 (x + 11)

Step 1: Find the rates of change for each ordered pair. Example: Boiling Point of Water Altitude Temp. 8000 197.6 4500 203.9 3000 206.6 2500 207.5 Is the relationship shown by the data in the table linear? If so, model the data with an equation. Step 1: Find the rates of change for each ordered pair. Step 2: Use the slope and a point to write an equation.

Summary Slope - Int. Form Standard Form Point - Slope Form y = mx + b Ax + By = C y – y1 = m(x - x1) x and y are variables m = slope b = y-int. A, B and C are WHOLE Integers (x1 y1) is a point of the equation or graph

Wrap Up Point-Slope Form Graph Using Point-Slope form Start at the point Graph the slope Write equation in point-slope form Given a point and a slope Given two points Writing an equation from a table Find the rate of change (slope) Pick a point to plug in What two things are given to you in the point-slope form?