Linear Equations Objectives Find slope Graph Lines Write

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

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

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

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

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

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

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

Graph the line: 3 x – 2 y = 8 n Get y by itself: -2 y = 8 – 3 x y = -4 + 3/2 x n Plot y-intercept (this is the number by itself): Mark the point -4 on the y-axis (down 4) n 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 2 nd point (slope of 3/2) n Connect

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

Graph the line: x = 5 n When there is only an x the value of x for all points n n n 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 n In this case the y values always have to be the same. n (4, -2) n (-3, -2) n (0, -2) n Graph and connect these points, what do you find? n 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 n Y = mx + b n Put the slope in for the m. n Put the y-intercept in for the b n Y = -2/3 x + 5

Find the equation of the line that passes through (3, 5) and (-2, 4) 1. Find the slope: (y 2 – y 1) / (x 2 – x 1) (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 2.

Write the equation of the line passing through (4, -2) and (-2, 4) 1. Find slope: 1. 2. Find b: y = mx + b 1. 2. 3. m = (y 2 – y 1) /( x 2 – x 1) (4 - -2) / (-2 – 4) = 6/-6 = -1 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 1. 2. Put slope and y-intercept into equation. y = -1 x + 2

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

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

Application n 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. n S = 375 +. 05 x n 375 is set value with rate of change of. 05 for sales.

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