1. Section 6-: Point-slope Form of a Linear Equation SPI 22C: select the graph that represents a given linear function Objective: Graph and write linear equations in point-slope form 1. Slope-Intercept form: y = mx + b 2. Standard Form: Ax + By = C 3. Point-Slope form: y – y 1 = m (x – x 1 ) 3 Different Forms of a Linear Equation

2. y – y 1 = m ( x – x 1 ) Point-Slope Form of a Linear Equation one set of ordered pairanother set of ordered pair Slope of the linear equation

3. Graph the equation y – 2 = (x – 1). Step 2. Write the slope (m). Graph a Linear Equation in Point-Slope Form 1313 y – y 1 = m (x – x 1 ) (2, 1) Step 1. Write the (x, y) ordered pair. 1313 Step 3. Graph the equation plot ordered pair first use slope from known point draw solution line

4. y – = (x – ) Write the equation of a line with slope -3 that passes through the point (-1, 7). Write a Linear Equation in Point-Slope Form y – y 1 = m (x – x 1 ) What is the slope in the problem?-3 What is the point in the problem?(-1, 7) (-1) 7 Simplify y – 7 = -3(x + 1)

5. Write an equation for the line in point- slope form. Use Two Points to Write an Equation (Point-slope Form) y – y 1 = m (x – x 1 ) Step 1. Locate any two points (-1, 4) and (2, 3) Step 3. Use either point to write an equation. Step 2. Use the points to find the slope Simplify

6. Write an Equation using a Table xY 4 36 57 1110 Is the relationship shown in the table linear? If so, model the data with an equation. Step 1. Find the rate of change of consecutive ordered pairs. (If the rate of change is the same, then the data is linear). 3 – (-1) = 4 5 – 3 = 2 11 – 5 = 6 6 – 4 = 2 7 – 6 = 1 10 – 7 = 3 Rate of Change Change in y Change in x 2 4 = 1 2 1 2 = 1 2 3 6 = 1 2 Rate of change is the same, so the data is linear

7. Continued.... xy 4 36 57 1110 Is the relationship shown in the table linear? If so, model the data with an equation. Step 2. Model the data with an equation Recall: Rate of change (slope) is ½. 1 2 y – y 1 = m (x – x 1 ) y – = (x – ) Use any ordered pair, from the table, to complete the equation 57

8. y – = (x – ) Real-world and Tables of Data TemperatureCalories 68°3030 62°3130 56°3230 50°3330 The table at the right represents the amount of calories burned per day when working outdoors at the stated temperature. Is the relationship shown in the table linear? If so, model the data with an equation in point slope form. Step 1. Is the data linear? If so, what is the rate of change? Step 2. Write an equation in point-slope form. 503330