y = mx + c Flashcards
What does m stand for?
Gradient
What does c stand for?
y-intercept
How do you calculate the gradient?
Rise / Run
or
Difference in y’s / Difference in x’s
What are the steps to see if a coordinate is on, above or below the graph of a given equation?
Take the x value from the coordinate.
Substitute this into the equation.
Workout what the y value should be.
Compare it to the y value in the coordinate to determine if it is on, above or below the graph.
How do you find the equation of a parallel line from a given equation?
Find the gradient from the given equation.
Parallel gradients are the same.
Put this in the form y=mx+c choosing any different value for c.
How do you find the equation of a parallel line from a given equation,
going through a given coordinate?
Find the gradient from the given equation.
Parallel gradients are the same.
Put this in the form y=mx+c
c is found by substituting the x and y values (from the coordinate) into the new y=mx+c and solving.
How do you find the equation of a perpendicular line from a given equation?
Find the gradient from the given equation.
For perpendicular gradients, change the sign and flip it. (negative reciprocal)
Put this new gradient in the form y=mx+c
Put this in the form y=mx+c choosing any value for c.
How do you find the equation of a perpendicular line from a given equation,
going through a given coordinate?
Find the gradient from the given equation.
For perpendicular gradients, change the sign and flip it. (negative reciprocal)
Put this new gradient in the form y=mx+c
c is found by substituting the x and y values (from the coordinate) into the new y=mx+c and solving.
Where would you find the gradient of the line from an equation?
It is the number (and sign) in front of the x,
when y is the subject.
(y=mx+c)
Where would you find the y-intercept of the line from an equation?
It is the number (and sign) on its own,
when y is the subject.
(y=mx+c)
How do you find the gradient and y-intercept from
6x + 2y = 7
Rearrange the equation into the form y=mx+c
Subtract 6x from both sides
2y = -6x + 7
Divide both sides by 2
y = -3x + 3.5
Gradient m = -3
y-intercept c = 3.5
How do you find the equation of a line passing through the two points A and B?
A = (4,7) B = (9,17)
Find the gradient using Rise/Run.
m = 17 - 7 / 9 - 4
m = 10 / 5
m = 2
Put it in the form y=mx+c
Substitute the x and y values from one of the coordinates to find c
y = 2x + c
7 = 2(4) + c
7 = 8 + c
-1 = c
Write in the form y=mx+c
y = 2x - 1
(4 , y ) is on the line of
y = 3x + 5
How do you find the y coordinate?
Substitute the x vale into the equation and solve.
y = 3x + 5
y = 3(4) + 5
y = 12 + 5
y = 17
(4 , 17 ) is a point on the line
How do you find the equation of the line
with a gradient of 5
going through the point (3, 11)?
Put the gradient into the form y = mx + c
y = 5x + c
Substitute the x and y values from one of the coordinates to find c
11 = 5(3) + c
11 = 15 + c
-4 = c
Write in the form y=mx+c
y = 5x - 4
How do you find the equation of the line
Find the gradient m by using Rise/Run.
Find the y-intercept c where the graph crosses the y-axis.
Put m and c in the form y=mx+c
How do you find the equation of the line
Find the gradient m by using Rise/Run.
Find the y-intercept c where the graph crosses the y-axis.
Put m and c in the form y=mx+c
How do you find the equation of the line
Find the gradient m by using Rise/Run.
Find the y-intercept c where the graph crosses the y-axis.
Put m and c in the form y=mx+c
How do you draw the graph of
y = 3x - 2
Use y=mx+c to find the gradient m and the y-intercept c.
Start with c at -2 on the y -axis.
The gradient m is Rise/Run (Run of 1, Rise of 3) from point c.
Plot a few points and then join them with a straight line.
How do you draw the graph of
y = (3/2)x + 1
Use y=mx+c to find the gradient m and the y-intercept c.
Start with c at 1 on the y -axis.
The gradient m is Rise/Run (Run of 2, Rise of 3) from point c.
Plot a few points and then join them with a straight line.
How do you draw the graph of
y = -(1/2)x + 6
Use y=mx+c to find the gradient m and the y-intercept c.
Start with c at 6 on the y -axis.
The gradient m is Rise/Run (Run of 2, Rise of -1 = DOWN) from point c.
Plot a few points and then join them with a straight line.
