Y12 005 Equation of a Line & Coordinate Geometry

Question 1

A Cartesian plane is …

Answer 1

…the x-y coordinate plane.

Question 2

How would you check if a point lies on a line / curve?

Answer 2

Substitute in the coordinate to check if it satisfies the equation.

Question 3

How do you find the x-intercept?

Answer 3

Substitute y = 0.

Question 4

How do you find the y-intercept?

Answer 4

Substitute x = 0.

Question 5

What kind of graph has an equation of the form y = mx + c and what is given by m and c?

Answer 5

A straight-line graph with gradient m and y-intercept c.

Question 6

What is the gradient and y-intercept of:

Answer 6

gradient = 3
y-intercept = 8

Question 7

What is the gradient and y-intercept of:

Answer 7

gradient = -3/2
y-intercept = 5

Question 8

What is the gradient and y-intercept of:

Answer 8

gradient = -4/5
y-intercept = 3/5

Question 9

What is the relationship between the gradients of parallel lines?

Answer 9

They are the same.

Question 10

What is the relationship between the gradients of perpendicular lines?

Answer 10

Question 11

Are these parallel, perpendicular or neither?

Answer 11

Question 12

Are these parallel, perpendicular or neither?

Answer 12

Question 13

Are these parallel, perpendicular or neither?

Answer 13

Neither. The equations represent the same line.

Question 14

How would you find the equation of the perpendicular bisector of the straight line joining two points?

Answer 14

Question 15

What is ‘intersect’ a trigger word for?

Answer 15

Simultaneous equations.

Question 16

Answer 16

Question 17

What form does a linear model take?

Answer 17

Question 18

For linear model y = ax + b, interpret the meaning of the constants a and b.

Answer 18

As x increases by 1 y increases by a.
y = b when x = 0.

For a given real-life model interpret the real-life meaning of these.

Question 19

Don’t forget to include UNITS in your modelling answers.

E.g. £, m, g, elephants

Answer 19

Not a question, just a common mistake.

UNITS, UNITS, UNITS, UNITS, UNITS, UNITS, UNITS, UNITS, UNITS

Question 20

Answer 20

Question 21

Answer 21

Question 22

Answer 22

Question 23

Answer 23

If they use the 5 first on the numerator then they should use the -1 first on the denominator.

Question 24

Answer 24

Question 25

Answer 25

Question 26

Answer 26

1. Only (c) is correct.

Question 27

Answer 27