Warm Up 1) Graph the line y = -3 2) You drive 60 miles in 2 hours and 150 miles in 5 hours. What is the rate of change and what does it represent?

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Presentation transcript:

Warm Up 1) Graph the line y = -3 2) You drive 60 miles in 2 hours and 150 miles in 5 hours. What is the rate of change and what does it represent?

Point – Slope Form y – y 1 = m(x - x 1 ) y – coordinate x – coordinate Example: y – 6 = 3(x – 5) Goes through point (5, 6) and has slope of 3 SLOPE

Point-Slope Form (x, y) (x 1, y 1 ) = (-2, -2) 1. Write the equation in Point-Slope Form of the graph below:

Graphing Using Point-Slope Form 2. Graph the equation

Graphing Using Point-Slope Form 3. Graph the equation

Write an Equation in Point-Slope Form Given a Point and a Slope 4. (-1, -3); Slope = 4 y + 3 = 4(x + 1) 5. (-10, 0); Slope = 2 y = 2(x +10) 6. (-4, 3); Slope = -6 y – 3 = -6(x +4)

Steps: 1. Find the slope between the two points. 2. Pick one point to use in order to write the equation. 3. Plug in the slope and coordinate from the point into the Point-Slope Form Write an Equation in Point- Slope Form Given Two Points

7. (-3, 6) and (1, -2) y – 6 = -2(x + 3) or y + 2 = -2(x – 1) 8. (-2, 3) and (-1, 1) y – 3 = -2(x + 2) or y – 1 = -2(x + 1) 9. (-2, -5) and (7, -6) y + 5 = - (x + 2) or y + 6 = - (x – 7) Write an Equation in Point- Slope Form Given Two Points

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 the relation? (-11, -7), (-1, -3), (4, -1), (19, 5) What is a possible equation in Point-Slope Form? y + 7 = 2/5 (x + 11)

Example: AltitudeTemp Boiling Point of Water 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.

Ex Identify the form of each equation. Change into the stated form. 1) y = -½x + 3 2) 2x – 3y = 6 3) y – 1 = - (x + 6) Standard Slope-intercept Slope-intercept & Standard

Summary Slope - Int. Form Standard FormPoint - Slope Form y = mx + bAx + By = Cy – y 1 = m(x - x 1 ) x and y are variables m = slope b = y-int. A, B and C are WHOLE Integers (x 1 y 1 ) 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?