Slopes of lines

GraphingEquation of

Slope and SteepnessRate

Parallel and Perpendicular

Graphing

1. You could make a table of points, plot the points and connect with a line, sub in x value and solve for the y value

2. If it is in the slope intercept form1. Plot the y-intercept (b value) on the y axis2. From y intercept do the slope, rise over run of

the line

Graphing Continued

Positive Sloping lines should go up from left to rightIf you are at the top of the page remember

you could have both the rise and run be negativeKey is do both rise and run the same

Negative Sloping lines should go down from left to right

You can do either the rise or the run negative, not both

Solve for y and graph

Get y-variable by itselfMove all terms without a y to the other sideDivided everything by the coefficient of the y-termWrite in order of y = mx +b

Slope

12

12

xx

yy

x

y

run

riseslopem

If you have the graph of a line, you can connect two points on the line making a triangle to get the rise and the run of the line

Steeper the slope the farther away from 1 it will beShallower the slope the closer to zero it will beNo slope or constant rate is a horizontal line

Rate – when comparing two quantities, miles per hour

Always have slope written in simplest fractional form, not mixed but simplified

Slope intercept form of a line

M is the slopeB is the y-intercept, where the line crosses the y-axisX and y represent all ordered pairs that make the equation true

Writing the equation of a line in Slope Intercept form

1. If given slope and y-interceptSub in the values for m and b, sign of the intercept will be the

operation

2. Given the slope and a pointSub in the value for m, x and y, and solve for the b valueSub in the values for m and b, sign of the intercept will be the

operation

3. Given two points – line of best fitFind the slope, by using slope formulaSub in the value for m, x and y, and solve for the b valueSub in the values for m and b, sign of the intercept will be the

operation

Intercepts

Y-intercept – where line crosses the y axisTo find it set x=0 and solve for y(0,y)

X-intercept – where line crosses the x axisTo find it set y=0 and solve for x(x,0)

Parallel and Perpendicular Lines

Parallel lines – two lines that never intersectSlopes of the lines are exactly the sameHave different y-interceptsIf the y-int is the same then it would be the same

linePerpendicular Lines – two lines that intersect and form a right angle

Slopes are opposite reciprocals, one positive the other is negative, num and denom are flipped

They can have the same y-int