Math- Slopes

Slope Intercept

y=mx+b

• m is slope

• b is y-intercept

  • where x is 0 and where it passes through the y-axis

• This form of a linear equation shows the relationship between the variables, plotting the line on a graph.

Point Slope

y-y1=m(x-x1)

• x1 and y1 are coordinates (x,y)

• they are negative in the equation but are positive (vice versa if adding in equation)

• can use any coordinates

• can be turned into slope intercept → standard form (if necessary)

• you can graph from point slope

  • go to the coordinate point then count the slope from there

Standard Form

Ax+By=C

• A,B,C are integers (no fractions/decimals)

• A and B are not both 0

  • They can individually be 0 but not at the same time

• A is always positive

  • If A isn’t positive then multiply everything by a negative

• if A=0 then the line is horizontal

• if B=0 then the line is vertical

• to convert to slope intercept, solve for y

  • subtract Ax both sides then divide by B by all terms

Things to Remember

• m= change in y/ change in x

• slope = 0

  • EX. 0/2 = 0, slope is horizontal (y= number)

• slope=undefined

  • EX. 2/0 = undef., slope is vertical (x= number)

• when converting from standard to slope-intc, be careful of dividing + double check if it is correct

• when using a table to find a slope, just solve it like m=, less room for error → more efficient

Parallel

2 lines are parallel when:

• the 2 lines have to have the exact same slope

• if the slope is a negative from the other, its not parallel

perpendicular

2 lines are perpendicular when:

• they have the negative reciprocal of the other

  • Ex. y=-2x+3

  • y=1/2 +5

• to find it, just take the negative of the slope, in this case -2 so it would be 2, and then flip it so that number is now on the top or bottom → ½

• the y intercept doesn’t matter for perpendicular lines, it has to intersect somewhere (supposedly the line is continuous and never ends)