Graphing Lines 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, and standard form
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) is what form?
Point Slope
y=mx+b what form?
slope intercept
Ax+By=C What form?
Standard Form
Why is it called “point-slope” form?
It has a hidden point (x,y) and a slope (m) in it
Why is it called “slope-intercept” form?
It has a slope (m) and an intercept (b) 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 X-Intercept in Standard Form?
Use ( C over A, 0) to get the x intercept.
How do you find the slope in Standard Form?
m = -A/B (opposite of A over B)
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 are the slopes of the diagonals of a square?
+1 and -1
A slope of 1/10 is closer to (zero or one)
zero
A slope of 7/8 is closer to (zero or one)
one
what do you call something that goes straight up and down?
VERTICAL
What dod you call something that goes from left to right?
HORIZONTAL (like looking along the horizon)
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)
the equation for the slope of the line is (if you have two points)
m = y-y / x-x
People think of the slope as _____ over _____
RISE, RUN
What is the name of the point (0,0) ?
origin
What is the equation of a perfect positive diagonal going through the 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.
How can you think about 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
Name the FORM, name a POINT and name the SLOPE: y = 2/3 x - 5
SLOPE INTERCEPT, (0,-5), 2/3
Name the FORM, name a POINT and name the SLOPE: 5x + 4y = 40
STANDARD, (0,10)or(8,0), -5/4
Name the FORM, name a POINT and name the SLOPE: y-7 = 1/2 (x+8)
POINT SLOPE, (-8,7), 1/2
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
What is a way to remember how to plot points like (-2,4) or (7, 8)
WALK x then CLIMB y
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 0.0001 is closer to (zero or one)
zero
A slope of 5 is closer to (one or undefined)
undefined (straight up and down)
What does VERTICAL mean?
goes straight up and down
What does HORIZONTAL mean?
goes from left to right
What is the origin?
(0,0)
WHat does the line y=0 look like?
it is the x axis (all of the points on the x axis have a y value of Zero
What does the line x=0 look like?
it is the y axis (all of the points on the y axis have an x value of ZERO)
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 (0,0)
What is the equation of the x axis?
y=0
Wat is the equation of the y axis?
x=0
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? What can you do?
Use algebra to rearrange it
What form? y = 4x - 3
slope intercept
What form? y - 3 = 2( x-8)
point slope
What form? 4x-2y=7
standard
Name the FORM, name a POINT and name the SLOPE: y = 3x
special form with a slope of 3 through the origin, or change to y=3x+0 SLOPE INTERCEPT (ZERO INTERCEPT). (0,0), 3
Name the FORM, name a POINT and name the SLOPE: y = 7
special horizontal through (0,7), or change to y=0x+7 SLOPE INTERCEPT (ZERO SLOPE), (0,7), zero
Name the FORM, name a POINT and name the SLOPE: x = 9
special none. vertical line. (9,0), undefined
Name the FORM, name a POINT and name the SLOPE: y-5 = 4(x -6)
POINT SLOPE, (6,5), 4
Name the FORM, name a POINT and name the SLOPE: 5x - 5y = -10
STANDARD, (0,2) or (-2,0), slope of 1
Name the FORM, name a POINT and name the SLOPE: y = 3x + 2
SLOPE INTERCEPT, (0,2), 3
Name the FORM, name a POINT and name the SLOPE: y = Hx - G
SLOPE INTERCEPT, (0, -G), H
Name the FORM, name a POINT and name the SLOPE: y - M = Z (x + T)
POINT SLOPE, (-T, M), Z
Name the FORM, name a POINT and name the SLOPE: Px + Ry = H
STANDARD, (0, H/R) or (H/P, 0), -P/R
Name the FORM, name a POINT and name the SLOPE: y = W
special horizontal. POINT SLOPE (ZERO SLOPE), (0,W), zero
Name the FORM, name a POINT and name the SLOPE: x = B
none, special vertical line, (B,0), undefined
Name the FORM, name a POINT and name the SLOPE: y = Qx
special slope intercept, the intercept is zero. Point (0,0), SLOPE (Q)
How do you find the Y-Intercept when given Standard form?
Use (0, C over B) to get the y intercept and
