Pre-Algebra Chapter 8 Sections 4 & 5 Quiz

How to find the slope of the line Remember – the slope is rise run So – to find the slope you subtract the rise numbers of the ordered pair: the y axis numbers. The answer is the rise. Then you subtract the run numbers of the ordered pair: the x axis numbers. The answer is the run.

Find the slope of a line For example if the questions asks: find the slope of the lines: And you are given a graph that shows the ordered pairs as (0,5) and (-1, 7). You first subtract 5 – 7 = 2. The RISE is 2 Subtract = remember that two negative signs right together become a positive so you have = 1. The RUN is 1

Find the slope of a line So the slope of the line = 2/1

Negative/Positive/Zero/Undefined If the questions asks you to determine if the line is negative/positive/zero/or undefined: First find the slope of the line (see previous slides) Then determine which way the line would go if you were to graph the line. If it is going uphill the line is POSITIVE. If the line is going downhill, the line is NEGATIVE.

Positive/Negative/Zero/Undefined If the rise = 0 that means the line is straight across. There is NO RISE so the slope is ZERO. If the RUN is 0 that means the line will go straight up and down – there will be no movement horizontally. This line is UNDEFINED.

Slope and Y-Intercept This equation is in slope intercept form: Y = 2x + 3 This equation IS NOT in slope intercept form: 2x + y = 3 If an equation IS NOT in slope intercept form then you will need to put it in slope intercept form. To do this you must move the y to one side of the = by itself – it cannot have another number with it.

Slope and Y-Intercept So … in the case of the equation: 2x + y = 3 First – I move the 2x to the other side of the = sign by doing the opposite function. 2x is positive so I’m going to SUBTRACT 2x from it: 2x – 2x + y = 3 – 2x Now I have y = 3 – 2x

Slope Intercept Form Now, y = 3 – 2x is in slope intercept form which means: The y-intercept is 3. In slope intercept form the y-intercept IS ALWAYS the constant (the number without a variable). The slope is -2. In slope-intercept form the slope IS ALWAYS the number with the variable.

Slope-Intercept Form If the equation looks like this: 2y + 3x = 10 It IS NOT in slope-intercept form because the y is on the same side as 3x AND it has a coefficient– the 2. First, I have to put the equation in slope intercept form.

SLOPE-INTERCEPT FORM 2y + 3x = 10 First – move the 3x to the other side. Do this by subtracting 3x from BOTH sides: 2y + 3x – 3x = 10 – 3x I now have: 2y = 10 – 3x The equation is NOT in slope intercept form yet. The y still has a 2 with it.

Slope-Intercept Form 2y = 10 – 3x Now to get rid of the 2 and since the way it is written tells me it is a multiplication problem I do the opposite of that – which is division and divide all terms by 2: 2y = 10 – 3x 2y 2 2

Slope-Intercept Form I now have: y = 5 – 3x 2 The y-intercept is 5 and the slope is -3x 2

Parallel and Perpendicular Lines The slope we are using is -2/1. In this equation the y-intercept was 3. So, graph the 3 Then you use the slope to find the next Place on the graph. The slope -2/1. This means you would go DOWN from the star two points and OVER 1 point. The line is going DOWNHILL which means there is a negative slope.

Parallel and Perpendicular line I have made a graph of the slope -2/1 I know the line is negative because it goes downhill. Now, I need the slope of the parallel line. Since a parallel line runs right along side the other line (that’s what parallel means), the slope of the PARALLEL line is the same as the original line: -2/1. To find the slope of the PERPENDICULAR line (which is defined as an intersecting line) the slope is the opposite sign and the invert of the slope: +1/2.

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