Linear Equations Objectives: Find slope Graph Lines Write equation in slope-intercept and general form

Slope The slant of a line is called its slope. Slope is measured by its rise as compared to its run. Rise / Run Rise is the vertical change in the line Run is the horizontal change in the line Mathematically you can find rise by subtracting the y’s Mathematically you can find run by subtracting the x’s.

Slope Formula: m = (y2 – y1) / (x2 - x1) Find the slope of the line that passes through the points (2/5, -1/2) and (3/4, 1/3) (-1/2 – 1/3) / (2/5 – ¾) need common denominator (-3/6 – 2/6) / (8/20 – 15/20) (-5/6) / (-7/20) when dividing fractions invert and -5/6 x -20/7 = 100/42 multiply 50/21 reduce

When calculating slope if the rise is 0, called ‘0 slope’, the line is horizontal (No RISE). When calculating slope if the run is 0, called ‘no slope’, the line is vertical (NO RUN)

When the slope of a line is positive, the line slants up from left to right. When the slope of a line is negative – the line slants down from left to right. When the slope of a line is 0 – the line is horizontal. When the slope of a line is ‘no slope’ – the line is vertical.

Find the slope of the line passing through (1,2) and ((5, -3) (-3 – 2) / (5 – 1) => -5 / 4 (2/3, -4) and (2/3, -2) ( -2 - -4) / (2/3 – 2/3) => 2 / 0 = no slope

Slope-Intercept Form: y = mx + b In slope intercept form the number with the x (m) is the slope. The number by itself it the y-intercept. Find the slope and y-intercept of 3x + 2y = 6 Get y by itself: 2y = 6 – 3x Subtract 3x from both sides Y = 3 – 3/2 x Divide both sides by 2 Slope: - 3/2 Y-intercept: 3

Graph the line: 3x – 2y = 8 Get y by itself: -2y = 8 – 3x Plot y-intercept (this is the number by itself): Mark the point -4 on the y-axis (down 4) Count slope (this is the number with the x – numerator is rise, denominator is run) from this point: From this point go up 3 and right 2 and plot a 2nd point (slope of 3/2) Connect

Graph the line that contains the point (5, -3) and has a slope of -4/5 Mark the point (5, -3) on the coordinate plane. Right 5 and down 3 From this point count your slope (-4/5) Down 4 and right 5 Connect the two points

Graph the line: x = 5 When there is only an x the value of x for all points have to be that number. For example (5,2) (5,-3) (5,0) Connect these points. What do you find? When only an x in the equation the graph is a vertical line through that value.

Graph: y = -2 In this case the y values always have to be the same. (4, -2) (-3, -2) (0, -2) Graph and connect these points, what do you find? The graph of an equation with only an x is a horizontal line at that value.

Find the equation of the line with slope of -2/3 and y-intercept of 5 Y = mx + b Put the slope in for the m. Put the y-intercept in for the b Y = -2/3 x + 5

Find the equation of the line that passes through (3, 5) and (-2, 4) Find the slope: (y2 – y1) / (x2 – x1) (5 – 4)/(3 - -2) = 1/5 Use the slope and one point to find the b y = mx + b substitute point and slope into equation 5 = (1/5)(3) + b solve for b 5 = 3/5 + b 22/5 = b 3. Write the equation y = mx + b y = 1/5 x + 22/5 put slope and y-intercept in

Write the equation of the line passing through (4,-2) and (-2, 4) Find slope: m = (y2 – y1) /( x2 – x1) (4 - -2) / (-2 – 4) = 6/-6 = -1 Find b: y = mx + b Put slope and one of points in and solve for b. 4 = (-1)(-2) + b 4 = 2 + b 2 = b Write equation: y = mx + b Put slope and y-intercept into equation. y = -1x + 2

Horizontal Lines Find an equation of the horizontal line containing the point (3,2) Horizontal lines – have no rise so y is constant. Equations are in the form y = # In this example the equation would be y=2.

Vertical Lines Find the vertical line passing through (3,2) Vertical lines have no run so the x remains constant. X = # In the example the equation would be x=3

Application Don receives $375 per week for selling new and used cars at a car dealership in Oak Lawn, Illinois. In addition he receives 5% of the profit on any sales he generates. Write an equation that relates his weekly salary, S, when he has sales that generate a profit of x dollars. S = 375 + .05x 375 is set value with rate of change of .05 for sales.

Assignment: Page 191 #9, 13, 17, 21, 25, 31, 35, 39, 41, 47, 53, 67, 75, 79