1. Warm-Up 1. Rewrite -5x – 7y = 10 to find the slope and y-intercept. 2. Find the x-intercept of 4x – 6y = -64 3. Write the equation of a line in slope- intercept form that goes through the points (-3, -15) and (4, 6)

2. HW Check – Word Problems

3. 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

4. Overview for today… Point-Slope Form Graphing Using Point-Slope Form Writing an Equation in Point-Slope Form Writing an Equation Using a Table Forms we’ve learned so far… Slope-Intercept Form: y = mx + b Standard Form: Ax + By = C

5. Point-Slope Form y – y 1 = m(x – x 1 ) m = slope (x 1,y 1 ) = a point that the line goes through Best used 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.

6. Point – Slope Form y – y 1 = m(x - x 1 ) y – coordinate x – coordinate Goes through point (5, 6) and has slope of 3 Example: y – 6 = 3(x – 5) SLOPE Write the equation in point-slope form that

7. Point-Slope Form (x, y) 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:

8. 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)

9. 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

10. 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

11. 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

12. 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)

13. Example: AltitudeTemp. 8000197.6 4500203.9 3000206.6 2500207.5 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.

14. 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

15. 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?