Sec 3 Graphs Flashcards
How do you find the equation of a line from two points
1- Use diff. in y/ diff. in x, to find the gradient of the line
2- Sub. this into the equation y=mx+c
3- Sub. the points into the equation
4-rearrange the equation to find ‘c’
5- Sub back into y=mx+c
Find the equation of the line that passes through the points (-2,9) and (3,-1)
a) What are the three methods for Drawing straight line graphs?
b) Explain these methods
Table of values:
1- Draw up a table with suitable values of x
2-Find the y values by sub.ing each x value into the equation
Using y=mx=c:
1- Rearrange the equation into the form y=mx=c
2- Put a dot on the y axis for the value of c
3-Using ‘m’ go up/down and left/right the correct no of units. e.g. If ‘m’ is +1/2, Go 2 right, 1 up.
4-When you have several dots draw a line through them.
5-Check gradient looks right
Skething Line Graphs:
1- Set x=0 in the equation , and find y ( where it crosses the y axis)
2- Set y=0 in the equation, and find x (where it crosses the x axis)
3- Mark the points on the line and draw a line through them.
Draw a graph of y= -2x+4 using the table of values method
Draw the graph of 4y-2x= -4 using the y=mx+c method
Sketch the straight line graph of y=3x-5
How do you find the midpoint of a line segment?
Points A and b have the coordinates (7,4) and (-1, -2) respectively.Find the midpoint.
[(7+-1) /2,(4+-2) /2]
(6/2,2/2)
=(3,1)
How can you use ratios to find the coordinates of a point on a line?
1- Find the difference between the coordinates of A and B (diff. in x coord.s and diff. i y coord.s).
2-Look at the ratio you’ve been given which will tell you what fraction along the line A is to the point, C.
3- Multiply the diff in x and y coord.s by the fraction.
$- Add these to the coord.s of A to find C.
Point a has the coordinates (-3, 5) and Point B has coord.s (18,33). Point C lies on the line segment AB, so that AC:CB= 4:3.
Find the coord. of C.
How do you find the equation of a line parallel to another given line?
1- Find the gradient; it will be same as the other line’s gradient as oi is parallel
2- Sub this gradient and the coordinate given (for x and y values) into the eqation y=mx+c
3- Solve to find ‘c’
How do you find the perpendicular line of a given line given a coordinate.
1- Find the perpendicular gradient by changing the sign and finding the recipricol.
2- Sub this into the equation y=mx+c along with the x and coordinate you’ve been given.
3- Solve to find ‘c’
4-Write the equation
1) How can you tell a graph is quadratic from its equation?
2) How do you plot a Quadratic graph?
1) It has an x^2 in it.
2)
- Draw an appropriate table of values (e.g.-4 to 4).
- Sub. each x value into the given equation to get each y value.
- Plot the points and draw a smooth curve.
- Dont count anomyles
How do you sketch a quadratic graph?
1- Solve the equation to find the x-intercepts
2-
- To find the turning point of the curve find halfway between the x intercepts. (add them together and /by two)
- Sub this x value into the equation.
- The x coord is the one you sub.ed into the equation and the y coord is the no. you get from solving the equation.
3- Sketch
Skecth the graph of -x2-2x+8=0
What are the features of exponential graphs?
e.g.
The graph shows how the number of victims of an alien virus (N) increases in a science fiction film. The equation of the graph is N=fgt
Where t is the no. of days in the film and f and g are +ive constants. Find the values of f and g.
a) Equations for reciprocal
b) What are the features of a reciprocal graph?
a) 1/x y=A/x xy=A
What are the features of sine and cos gaphs?
What are the features of tanx graphs?
a) How do you use a graph to estimate the solutions/roots to an equation (e.g. sinx=0.7) between to two limits (e.g. -180º and 180º)
b) Use the graph y=sinx to to estimate the solutions to sinx=0.7 between -180º and 180º
1) If the equation states sinx= (rather than y) draw a line across the point on the y axis where the equation equals to.
This is the graph of that equation.
2) Look at where this graph crosses a sin graph ( y=sinx)
The graph of y=2x2-3x is shown below.
a) Use the graph to estimate both the roots of 2x2-3x=7
b) Find the equation of the line you would need to draw on the graph to solve 2x2-5x+1=0
a) What is the format of the graph in graph transformations?
b) Where does the position of the variable tell you to move?
c) How are reflected grahs represented?
a) y = f(x)
b) Inside : left/right (y axis) , Outside : up/down (x axis)
c) -f(x) Reflect in x axis
f(-x) Reflect in y axis
For y=f(x) find:
y = f(x) +2
y = f(x) -2
y = f(x+2)
For y=f(x), find:
y = -f(x)+2
y = f(-x)-1
y = f(x-3)-1
