y = mx + c Flashcards

1
Q

What does m stand for?

A

Gradient

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2
Q

What does c stand for?

A

y-intercept

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3
Q

How do you calculate the gradient?

A

Rise / Run

or

Difference in y’s / Difference in x’s

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4
Q

What are the steps to see if a coordinate is on, above or below the graph of a given equation?

A

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.

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5
Q

How do you find the equation of a parallel line from a given equation?

A

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.

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6
Q

How do you find the equation of a parallel line from a given equation,
going through a given coordinate?

A

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.

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7
Q

How do you find the equation of a perpendicular line from a given equation?

A

Find the gradient from the given equation.

For perpendicular gradients, change the sign and flip it.

Put this new gradient in the form y=mx+c

Put this in the form y=mx+c choosing any value for c.

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8
Q

How do you find the equation of a perpendicular line from a given equation,
going through a given coordinate?

A

Find the gradient from the given equation.

For perpendicular gradients, change the sign and flip it.

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.

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9
Q

Where would you find the gradient of the line from an equation?

A

It is the number (and sign) in front of the x,
when y is the subject.
(y=mx+c)

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10
Q

Where would you find the y-intercept of the line from an equation?

A

It is the number (and sign) on its own,
when y is the subject.
(y=mx+c)

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11
Q

How do you find the gradient and y-intercept from

6x + 2y = 7

A

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

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12
Q

How do you find the equation of a line passing through the two points A and B?

A = (4,7) B = (9,17)

A

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

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13
Q

(4 , y ) is on the line of
y = 3x + 5

How do you find the y coordinate?

A

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

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14
Q

How do you find the equation of the line
with a gradient of 5
going through the point (3, 11)?

A

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

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15
Q

How do you find the equation of the line

A

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

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16
Q

How do you find the equation of the line

A

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

17
Q

How do you find the equation of the line

A

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

18
Q

How do you draw the graph of
y = 3x - 2

A

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.

19
Q

How do you draw the graph of
y = (3/2)x + 1

A

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.

20
Q

How do you draw the graph of
y = -(1/2)x + 6

A

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.