Linear relationships

Question 1

Formula of how to calculate the gradient.

Answer 1

Gradient= vertical distance divided by horizontal distance

Question 2

How can the gradient of the line AB be written?

Answer 2

Mab

Question 3

How do we figure out a if a line has a positive gradient?

Answer 3

Any line which slopes upwards from left to right has a positive gradient.

Question 4

How do we figure out if a line has a negative gradient?

Answer 4

Any line which slopes downwards from left to right has a negative gradient.

Question 5

How can the gradient for parallel line be figure out?

Answer 5

Parallel lines have the same gradient.

Question 6

What is the gradient of a horizontal line?

Answer 6

A horizontal line has m = 0.

Question 7

What is the gradient of a vertical line?

Answer 7

A vertical line has an undefined gradient.

Question 8

What is the equation for almost every line?

Answer 8

The equation of (almost) any line takes place as y=mx+c

Question 9

In the equation of y=mx+c what represents the gradient?

Answer 9

In the equation why y=mx+c the gradient is represents by m.

Question 10

In the equation y=mx+c what represents the y intercept?

Answer 10

In the equation y=mx+c the y intercept is represented by c.

Question 11

What is the y intercept?

Answer 11

The y intercept represents where the line cuts the axis.

Question 12

What is the origin?

Answer 12

Origin is a mathematical concept which is used to denote a point where all the axes(x,y,z) meet. It is denoted as (0,0) in two dimensions and (0,0,0) in three dimensions

Question 13

What are the steps to calculate the equation of a straight line given any two points on it?

Answer 13

1. Sketch the line
2. Find the gradient
3. Calculate the y-intercept (substitute into the equation y=mx+c)
4. Use gradient and y-intercept to write down the formula.

Question 14

Apart from y=mx+c what other forms can the equation of the line be written?

Answer 14

A linear equation is usually written as y = mx + c, but other letters can be used to form a linear equation.

                             y = ax + b and P = mt + c, could also represent straight lines.

Question 15

What is the formula to calculate the gradient m=v divided by h used for?

Answer 15

The formula gradient= vertical divided by horizontal can always be used to measure of how steep the line is.

Question 16

What is the more mathematical formula to calculate the gradient?

Answer 16

Mab=y2-y1 divided by x2 - x1.

Question 17

What is the general equation of a line?

Answer 17

The equation of any line can be written in the form Ax + By + C = 0.
This is called the General Equation of a line.

(the general equation of a line can be rearranged so that the gradient and y-axis are easier to be obtained)