 # 7-1 Slope Objectives: Find the slope of a line given the coordinates of two points on the line.

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7-1 Slope Objectives: Find the slope of a line given the coordinates of two points on the line

What is Slope? Steepness Change in Y Change in X Rise Run
Y=mx + b Amount of Slant

The Graph of y = mx +b Consider the graph of y = x - 2 y
5 4 3 2 1 -2 -3 -4 -5 y x Compare to the graph of y = ½x - 2 Compare to the graph of y=2x-2

The Graph of y = mx +b Consider the graph of y = x - 2 y
5 4 3 2 1 -2 -3 -4 -5 y x Compare to the graph of y = -x - 2 Compare to the graph of y = -2x - 2

Determining Slope Rise=1 Rise=12 Run =2 Run =4 Rise=6 Run =2 Slope=

Determining Slope Rise= 8 = -2 Rise= 0 Run = -4 Run = n Rise= -2

Determining Slope Rise= n Run = 0 The Slope is UNDEFINED

Determining Slope 5-(-6) = 11 6 2-(-4)
Find the change in the Y-coordinates by subtracting(rise) Pick 2 points on the line (2, 5) Find the change in the X-coordinates by subtracting(run) 5-(-6) = 11 6 (-4, -6) 2-(-4) Write as a ratio (rise/run)

Determining Slope Y1-Y2 Y2-Y1 m = X1-X2 X2-X1
In general, to find the slope given two points on a line: Subtract the Y-coordinates (rise) (x1, y1) Subtract the X-coordinates (run) Write as a ratio (rise/run) (x2, y2) Y1-Y2 X1-X2 Y2-Y1 m = = X2-X1

Slope Summary Positive Slope Slope = 0 Undefined Slope Negative Slope
Negative slope is a downer Negative Slope

7-2 Point slope form Objectives: Write an linear equation in point slope form given the coordinates of a point on the line and the slope of the line

Point-Slope form Slope rise/run X coordinate of known point
Y coordinate of known point

Point-slope form Write the equation of a line given the point (5,2)
with a slope of 3 m (x,y) y–y1=m(x–x1) Y–2= 3(x–5)

7-3 Writing equations in Slope-Intercept form
Objectives: Write a linear equation in Slope-intercept form given the slope and y intercept

Linear Equations (y = mx + b)
b = y-intercept plot (0,b) to get your first point m = slope written as a fraction slope = rise/run Lean right if positive Lean left if negative

7-3 y=mx+b Slope intercept form: The y intercept,
Where it crosses the y line The y coordinate The x coordinate Slope rise/run

Linear Equations (y = mx + b)
b = -3 (y-intercept) plot (0,-3) y = 1/3 x - 3 m = 1/3 (slope rise/run) positive leans right plot up 1, right 3 plot down 1, left 3 connect the points

Linear Equations (y = mx + b)
b = 2 (y-intercept) plot (0,2) y = -1/2 x + 2 m = -1/2 (slope rise/run) negative leans left plot up 1, left 2 plot down 1, right 2 connect the points

7-3 Given the slope m and the y intercept b
write an equation in slope intercept form m= -3 b= -2 Step1: write the equation y=mx+b y= -3x-2 Step 2: substitute the given numbers

7-3 The equation can then be graphed y= -3x-2 Rise 3 run to the left 1
m= -3 Fall 3 and run to the right 1

7-3 Subtract the 4x from both sides 4x-2y=8 -4x -4x
Sometimes you may have to manipulate the equation to get it in slope-intercept form Subtract the 4x from both sides 4x-2y=8 -4x -4x Divide all by -2 to isolate y 2 -4 -2y= -4x +8 -2 -2 -2 y=2x-4

Given two points, write the equation of a line in y intercept form
(2,-3) and (4,-2) Steps: 1. Find slope 2. Place a point and the slope in into point slope form 3. Distributive property 4. Additive property of equality

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