Four Types of Slope Positive Slope Negative Slope Zero Slope Undefined Slope Slope Dude will help us understand the 4 types of slope
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7 Four Types of Slope Positive Slope Negative Slope Zero Slope Undefined Slope Slope Dude will help us understand the 4 types of slope
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15 Direct Variation 1. What is it a. A linear equation that crosses through (0, 0) b. You may see it in problems written as: y varies directly with or as x 2. Equation a. y=kx b. k represents the constant of variation
16 You can solve an equation for y and see if it is in the form for a direct variation. Does the equation represent a direct variation? If so, find the constant of variation. 1. 7y = 2x 2. 3y + 4x = 8
17 When given that the relationship between two quantities is direct, you can write the equations by substituting the known values into the equation y=kx. Suppose y varies directly with x, and y = 35 when x = 5. What direct variation equation relates x and y? What is the value of y when x = 9?
18 The x and y intercept X-Intercept The point where a graph crosses the - axis. X-intercepts happen when the y-coordinate is zero. To find the x-intercept from an equation, replace y or f(x) with zero and solve for x. Y-Intercept The point where a graph crosses the - axis. Y-intercepts happen when the x-coordinate is zero. To find the y-intercept from an equation, replace x with zero and solve for y.
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21 When our equation is in slope-intercept form (y= mx + b), we can use the equation to find the and -intercept.
22 If the equation is NOT in slope intercept form, we can rearrange it and then find the and -intercept.
23 Identify the slope and y-intercept of the equation y = 3x - 2 y = -7x + 9 y=⅔x+2
24 Given the slope and y-intercept, write the equation m = 5 b = -9 m = -2 b = 8 m = ⅘ b = 17
25 Identify the slope and y-intercept of the equation y +3x = 15 2y -4x = 8 y + 8 = 5x
26 Graphing Using Slope Intercept Form 1) Equation MUST be in to graph. 2) Find (slope) and (y-intercept) 3) Plot (y-intercept) on the graph. **b is where you Begin. 4) Start at y-intercept and use (slope) to plot points for the line. ** is how many you Move **if m is positive, move and to the right. **if m is negative, move and to the right. 5) Draw a through the points.
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28 Standard Form of a Linear Equation Ax+By=C Special Rules: 1. A, B, and C cannot be fractions or decimals
29 The goal is to get the equation into the form Ax+By=C with no fractions! Get rid of the fractions Move x and y to the same side Change an equation into Standard From
30 You try... Write each equation in standard form: 1. y + 3 = 4(x-1) 2. y=¼x-2 3. y + 2 = ⅔ (x+4) The goal is to get the equation into the form Ax+By=C with no fractions! Get rid of the fractions Move x and y to the same side
31 You try Answers Write each equation in standard form: 1. y + 3 = 4(x-1) 2. y=¼x-2 3. y + 2 = ⅔ (x+4)
32 Graphing from Standard Form (Ax+By=C) Method 1 - Change to Slope Intercept Form and graph To change to Slope Intercept Form, just solve for y!
33 Graphing from Standard Form (Ax+By=C) Method 2 - Find and graph your x and y intercepts Find the y intercept a. Plug in 0 for x b. Solve for y Find the x-intercept a. Plug in 0 for y b. Solve for x Graph your intercepts and connect!
34 You try Example 1 Attempt using Method 1 Change to Slope Intercept Form Graph 3x + 5y = 15
35 You try Example 2 Attempt Method 2 Find the x and y intercepts Graph 3x + 5y = 15
36 Some things to notice about Standard Form In standard form, A, B, and C do not represent anything (unlike m and b in slope intercept form). It s just the equation rearranged in a different order with specific rules! You cannot just take an equation that s in standard form and graph it you have to either find the intercepts or switch it to slope intercept form!
37 So what s the point of Standard Form? Why even use it if A, B, and C don t really mean anything? Well standard form makes a lot of sense in a lot of word problems look at this example. We would write the equation 1x+12y = 60 where x represents songs and y represents movies. It s natural to write this equation in standard form! So we need to know how to evaluate equations in standard form :)
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44 Write an equation of the line in point slope form
45 Write the equation of the line that has a slope of 5 and passes through (-1, 5).
46 Write the equation of the line that has a slope of -1/3 and passes through (4,-7).
47 Write the equation of the line that passes through (1, 4) and (-2, 3).
48 Write the equation of the line that passes through (-2, 0) and (4, 1).
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