Math II 7.4 Slopey Stuff

Slope of a line (fancy definition) the ratio of the vertical change to the horizontal change as you move from one point to another.

Slope on a map If I go from one place to another it is how much I go up/down in comparison to how much I go left/right

Slope as a rate How much one thing changes, over how much something else changes.

Slope RISE RUN

Slope We use the variable M to represent slope

Find the slope Run rise We go up 3 We go Right 2 3 2

Find the slope Run rise We go down 1 We go Left 5 -5

Find the slope Run rise We go up 5 We go Left

What if we go the other way? Run rise We go down 5 We go right

Are they equal?

One last time! Run rise We go up 6 We go Right 1 6 1

What lines look like Positive slope Negative slope Slope is = 0 Slope is undefined

The formula Given two points: j (x 1, y 1 ) and k (x 2, y 2 ) Then the slope can be found using the following formula y 2 – y 1 x 2 – x 1 M=

y 2 – y 1 x 2 – x 1 M= j (3, 4) k (1, 5)

y 2 – y 1 x 2 – x 1 M= a (-2, 3) b (4, 4)

y 2 – y 1 x 2 – x 1 M= a (6, 3) b (-2, 3)

Parallel Lines Have the same slope! That means their slopes are = to each other

So, if Line AB has a slope of 2/3 Then any line parallel to line AB Has a slope of... 2/3

Perpendicular Lines Have negative reciprocal slopes

That means that if I multiply the slopes of perpendicular lines the answer will be -1. Is there an easier way to tell if they are perpendicular?

Two things... One – the slope is flipped over That’s the reciprocal part Two – the sign is changed Positive  Negative

So, if Line AB has a slope of 2/3 Then any line perpendicular to line AB Has a slope of... -3/2

An equation that represents a line is called a LINEAR EQUATION

Linear Equations Come in three different forms Standard Form Ax + By = C Point-Slope Form (y – y 1 ) = m(x – x 1 ) And our favorite…

Slope-Intercept Form y = mx + b slope y intercept

Identify the slope and intercept y = 3x + 4 slope y intercept

y = -2x + 5 slope y intercept

y = - x – 4 slope y intercept 4343

Identify the slope and intercept y = -3 slope No x so slope = 0 y intercept

x = 1 slope undefined y intercept No y so no y int ? ?

y + 7x = 4 Put in slope intercept form first y = -7x + 4 m = -7 and b = 4

What does it mean... If asked to write a linear equation in slope-intercept form? SOLVE FOR “y” Get “y” alone

y – 6x = -3 Write in slope-intercept form... Add 6x to both sides Is the y alone? Then you are done. +6x +6x y = 6x - 3

2y + 8x = 6 Write in slope-intercept form... subtract 8x from both sides Is the y alone? Then let’s keep going... -8x -8x 2y = -8x y = -4x + 3 Divide both sides by 2

Graph y = 3x +1 We go up 3 We go right 1 y int = 1 m = 3

Graph y = -2/3x + 3 We go down 2 We go right 3 y int = 3 m = -2/3

The end… kind of… The following slides cover some supplemental information about linear equations Proceed at your own risk YOU HAVE BEEN WARNED

You might think this is tricky... Write an equation of the line satisfying the given conditions

Slope = 3, goes through the point (-1,4) All we know is y = mx + b can we fill in 3 of the 4 things?

y = mx + b

Slope = 3, goes through the point (-1,4) 4 = 3(-1) + b 4 = -3 +b 7 = b

Slope = 3, goes through the point (-1,4) Since b=7 and m=3 The formula would be y = 3x+7

You might think this is tricky... Write an equation of the line satisfying the given conditions

Parallel to the graph of y = 2x-5 goes through the point (3,7) All we know is y = mx + b can we fill in 3 of the 4 things?

y = mx + b 7 = 2(3) +b Do we know yDo we know xDo we know m (slope)

Parallel to the graph of y = 2x-5 goes through the point (3,7) 7 = 2(3) +b 7 = 6 + b = b So our formula is y = 2x + 1

Is the point (2,8) on the line y = 3x+2 8 = 3(2) = = 8 Yes it is!!!!!!!

Is the point (3,5) on the line y = 5x+10 5 = 5(3) = = 25 No it is not!!!!!!!

Things to remember Slopes of parallel lines Slopes of perpendicular lines Horizontal lines Formula and slope Vertical lines formula and slope