Lecture 4

Question 1

Explain y=mx+c

Answer 1

The equation of a straight line on a graph

• x and y are the coordinates of any point on the line
• m is the gradient or slope of a line
• c is the point where the line intercepts the y axis – called the y intercept

Question 2

What is the equation of a line in a standard form?

Answer 2

Ax + By + C = 0

Question 3

What is the intercept?

Answer 3

The point(s) where the graph crosses the
axis

Question 4

How do you work out an intercept?

Answer 4

By setting one value to 0

Ex.
x - 3y = 12
2x – 3(0) = 12
2x = 12
x = 6
Thus, the x-intercept is: (6,0)

Question 5

What is the point-slope formula?

Answer 5

(y₂ – y₁) = m (x₂ – x₁)

Question 6

What is the gradient and what does it mean for the line?

Answer 6

How fast a line is rising or falling

A high value for m means a quick rise
A negative value for m means the line is falling

Question 7

How is the gradient worked out?

Answer 7

∆y/ ∆x
The difference in y divided the difference in x

Question 8

What is the equation of a circle?
What does it tell us?

Answer 8

(x-a)² + (y-b)² = r²

a and b shows the centre of the circle, the radius shows distance, x and y are points

Question 9

What happens to the circle equation if a=b=0?
What does it give us?

Answer 9

x² + y² = r²
This equation gives the distance between the centre and a point on the circle

Question 10

What is the general form of the circle?

Answer 10

x² + y² + Ax + By + C = 0
A,B and C are constants

Question 11

What is the equation for completing the square?

Answer 11

(a + b)² = a² + 2ab + b²
or
(a - b)² = a² - 2ab + b²

Question 12

What is a vertex?

Answer 12

A point where two straight lines meet