1. Recall: In the general equation m represents the slope, and b represents the y-intercept. For example: ½ is the slope and (0, -7) is the y-intercept In reverse, to write the equation of the line given the slope and y-intercept: Slope= -3 and y-intercept is (0,5)

2. Today we will learn how to “speed” graph using what we know about slope and y-intercept. For example: Given We will first identify the y-intercept as an ordered pair _________ Then we identify the slope as a fraction if it isn’t already _______ This will be our starting point on the graph

3. Second example when the slope is negative For example: Given We will first identify the y-intercept as an ordered pair _________ Then we identify the slope as a fraction if it isn’t already _______ This will be our starting point on the graph

4. a) Write the equation of a line that has a slope of and a y-intercept of b) Write the equation of a line that has a slope of and a y-intercept of

5. But the slope and y-intercept is NOT always given… But you CAN figure them out! Always look for the slope first… – Is it given? – Find it by looking at the ratio of rise over run If you know the slope, you can plug in the slope and a point (x and y) that you KNOW lies on the line, then you can solve for b…

6. Writing the equation of a line given the slope and not the y-intercept (using no graph). In other words, algebraically solving for b. For example: Write the equation of a line with a slope of and goes through the point. We know that is not the y-intercept because the ordered pair is not. First, identify everything you were given. m xy Then, plug in the m, x and y into the general equation of a line and solve for b. So the equation of the line is

7. Now you try!! Write the equation of a line with a slope of and goes through the point. m xy Again, identify everything you were given. Now plug in to Equation of the line is: __________

8. What if slope is a fraction….. Write the equation of a line with a slope of and goes through the point. Again, identify everything you were given. m xy Now plug in to Think of 4 as when multiplying it to So the equation of the line is:

9. Finding the slope between two points Given the points and We can find the slope between these two points with a generic slope triangle. Step 1) sketch an x and y axes Step 2) put the x values on the x axis and the y values on the y axis Step 3) determine how far apart the x values are and how far apart the y values are Step 4) plot both points and determine the rise over the run http://www.educreations.com/lesson/view/slope-between-two- points/6510072/?ref=appemail

10. Find the slope between the two points: x x yy x y 2 5 3 1 8 7 x x yy x y 2 -6 26 8