Graphing Linear Equations (all three forms) Flashcards
What is a linear equation?
It is a straight line (not a curve), and the x is not squared or cubed.
What are the three forms of a line?
slope-intercept, point-slope, standard
What is the point slope form?
y-y = m (x-x)
WHat is the slope intercept form?
y=mx+b
What is the standard form?
Ax+By=C
y-y=m(x-x) what form?
point slope
y=mx+b what form?
slope intercept
Ax+By=C What form?
standard
Why is it called “point-slope” form?
it has a hidden point and a slope in it
Why is it called “slope-intercept” form?
it has a slope and an intercept in it
How do you find the hidden point in point slope form? y-y=m(x-x)
to get your (x,y), take the opposite of the number next to the x to get your x, and take the opposite of the number next to the y to get your y
How do you find the points in Standard Form?
(0, __) to get the y intercept and (__,0) to get the x intercept.
How do you find the slope in Standard Form?
m = -A/B (opposite of A over B)
What is a trick to identify the correct form?
Look at the equal sign. What is to the left?
just a y ? then slope intercept
a y + or - something? then point slope
an X and a Y? then standard
How can you find the y intercept in any form?
You can always just plug a zero in for x and then solve for y. (0, __).
How can you find the x intercept in any form?
You can always just plug a zero in for y and then solve for x. (__ ,0)
What is a way to remember how to plot points like (-2,4) or (7, 8)
WALK x then CLIMB y
What are the slopes of the diagonals of a square?
+1 and -1
A slope of 2/3 is (steeper/less steep) than one.
less steep
A slope of -5/2 is (steeper/less steep) than negative one.
steeper
A slope of 1/10 is closer to (zero or one)
zero
A slope of 7/8 is closer to (zero or one)
one
A slope of 0.0001 is closer to (zero or one)
zero
A slope of 5 is closer to (one or undefined)
undefined (straight up and down)
If a line has a y intercept of 9, then the point _____ is on the line.
(0,9)
If a line has an x intercept of 9, then the point _____ is on the line.
(9,0)
If you are given two points, the equation for the slope of the line is
m = y-y / x-x
People think of the slope as _____ over _____
RISE, RUN
what form? y = 4x - 3
slope intercept
what form? y - 3 = 2( x-8)
point slope
what form? 4x-2y=7
standard
What is the origin?
(0,0)
What is the name of the point (0,0) ?
origin
Name the FORM, name a POINT and name the SLOPE: y = 2/3 x - 5
form: SLOPE INTERCEPT
point: (0,-5)
slope: 2/3
Name the FORM, name a POINT and name the SLOPE: 5x + 4y = 40
form: STANDARD,
point: (0,10)or(8,0),
slope: -5/4
Name the FORM, name a POINT and name the SLOPE: y-7 = 1/2 (x+8)
form: POINT SLOPE,
point: (-8,7)
slope: 1/2
Name the FORM, name a POINT and name the SLOPE: y = 3x
special form (through origin), or change to y=3x+0
form: SLOPE INTERCEPT (ZERO INTERCEPT).
point: (0,0)
slope: 3
Name the FORM, name a POINT and name the SLOPE: y = 7
special forms (horizontal), or change to y=0x+7,
form: SLOPE INTERCEPT (ZERO SLOPE),
point: (0,7)
slope: zero
Name the FORM, name a POINT and name the SLOPE: x = 9
form: special form. vertical line.
point: 9,0),
slope: undefined
Name the FORM, name a POINT and name the SLOPE: y-5 = 4(x -6)
form: POINT SLOPE
point: (6,5)
slope: 4
Name the FORM, name a POINT and name the SLOPE: 5x - 5y = -10
fprm: STANDARD,
point: (0,2) or (-2,0),
slope of 1
Name the FORM, name a POINT and name the SLOPE: y = 3x + 2
form: SLOPE INTERCEPT,
point: (0,2),
slope: 3
Name the FORM, name a POINT and name the SLOPE: y = Hx - G
form: SLOPE INTERCEPT,
point: (0, -G),
slope: H
Name the FORM, name a POINT and name the SLOPE: y - M = Z (x + T)
form: POINT SLOPE,
point: (-T, M),
slope: Z
Name the FORM, name a POINT and name the SLOPE: Px + Ry = H
form: STANDARD,
point: (0, H/R) or (H/P, 0),
slope: -P/R
Name the FORM, name a POINT and name the SLOPE: y = W
special form, horizontal, or change to y=0x+w,
form: POINT SLOPE (ZERO SLOPE),
point: (0,W),
slope: zero
Name the FORM, name a POINT and name the SLOPE: x = B
form: special form, vertical line,
point: (B,0),
slope: undefined
Name the FORM, name a POINT and name the SLOPE: y = Qx
special form, or change to y=Qx+0,
form: slope intercept, the intercept is zero.
Point (0,0),
SLOPE (Q)
WHat does the line y=0 look like?
it is the x axis
What does the line x=0 look like?
it is the y axis
What does the line y=x look like?
perfect positive diagonal through origin (0,0)
What does the line y= -x look like?
perfect negative diagonal through origin
What is the equation of the x axis?
y=0
Wat is the equation of the y axis?
x=0
What is the equation of a perfect positive diagonal going through tjhe origin?
y=x
WHat is the equation of a perfect negative diagonal going through the origin?
y=-x
What does the line y=4 look like?
horizontal (L to R) line through (0,4). up 4.
What does the line x=4 look like?
vertical (up and down) line through (4,0), to the right 4.
What does the line y = 1/2 x look like?
through origin (0,0) with slope of 1/2
Why are the A, B and C capital letters in Ax+By=C?
They have to be INTEGERS (whole numbers). This means that you won’t see 1/2x + 4/5y = 1/3. The A and B and C have to be integers like 4x-2y=9
What if a linear equation is not in one of the three forms?
use algebra to rearrange it
How can you think of the line x=5 to remember what it looks like?
It is all of the points that have an x value of five… so (5, 0), (5, 1), (5, 2), (5, 3), etc… straight up and down
How can you think about the line y=8 to remember what it looks like?
It is all of the points that have a y value of eight. So (0,8), (1,8), (2,8) ,(3,8), (4,8), (5,8)… All have a height of 8. Horizontal line up 8
How can you think of the points on the line y=x to remember what it looks like?
It is all of the points whose x and y are the same. (4,4), (10,10), (-5,-5), etc..
