Уроки математики и физики (RU + UA)

суббота, 18 августа 2018 г.

Lesson 18. Sloping lines


To graph a linear function:

1. Find 2 points which satisfy the equation
2. Plot them
3. Connect the points with a straight line

EXAMPLE:

y = 25 + 5x

SOLUTION:

Let x = 1 then
y = 25 + 5(1) = 30
Let x = 3 then
y = 25 + 5(3) = 40
EXAMPLE:

Draw the straight line 


y = x + 3.

Note

When working out the y-values, we usually write them in a table
Gradient

Have you ever seen sighs like this?
This is the gradient – how steep the hill is.
The “1 in 10” means that the hill goes up 1 m for every 10 m across.
Gradient = 1 in 10 = 1/10
The steeper the hill, the bigger the gradient.


EXAMPLE:

Find the gradient of this line.

EXAMPLE:

Find the gradient of this line.

Negative gradient

If a line slopes downwards to the right, it has a negative gradient.

Find the gradient of this line.negative because line sloping downwards to the right

The slope of a linear function

The steepness of a hill is called a slope. The same goes for the steepness of a line. The slope is defined as the ratio of the vertical change between two points, the rise, to the horizontal change between the same two points, the run.

The slope of a line is usually represented by the letter m. (x1, y1) represent the first point whereas (x2, y2) represents the second point.
It is important to keep the x-and y-coordinates in the same order in both the numerator and the denominator otherwise you will get the wrong slope.

EXAMPLE:

Find the slope of the line
(x1, y1) = (3, 2) and (x2, y2) = (2, 2)
A line with a positive slope (m ˃ 0), as the line above, rises from left to right whereas a line with a negative slope (m < 0) falls from left to right,

If two lines have the same slope the lines are said to be parallel.
You can express a linear function using the slope intercept form.

y = mx + b
m = slope
b = y – intercept 

Lesson 18

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