A point P is positioned relative to two perpendicular lines, called the coordinate axes. The perpendicular distance from the y-axis to point P is the x-coordinate, the perpendicular distance from the x-axis to point P. The coordinates x and y form an ordered pair (x, y).
(4, 3) is located 4 units from the y-axis to the right and 3 units above the
x-axis; the point (-2, 1) is 2 units to the left of the y-axis and 1 unit above
the x-axis. The distance, d, between the two points can be found by the
Pythagorean Theorem. The horizontal leg is the total distance inthe x-direction: 4 -
(-2) = 6; the vertical leg is the distance in the y-direction: 3 - 1 = 2.
The distance is then
d= 6 + 2=
A square has two corners of a diagonal at (6, 8) and (2,4). What is its area?
The difference in the x-direction is 6 - 2 = 4 and in the y-direction 8 - 4 = 4. The sides are both of length 4, so that the area is A = 4 x 4 = 16.
How do you measure the slant of a line? By definition, it is the ratio of the vertical change to the horizontal change (see figure below).
Forming the vertical change over the horizontal change (above) figure results in slope formula (where m is the slope).
m = y - b
x - a
- use this formula to calculate slopes of lines
What is the slope of this line?
To solve this problem, plug the digits in the line into the slope intercept equation.
m = y - b
x - a
y= 4, b = 2
= 5, a = 1
m = (4 - 2)
(5 - 1)
m = 2 = 1
The slope is 1/2.
Slope Intercept Formula
If you have a formula, such as x - 2y = 4, how do you calculate the slope of the line?
If you want
to graph a line, the formula to use is
y = mx + b
In this equation, m is the slope of the line and b is the y-intercept.
The y-intercept is when x = 0 in an equation.
The x-intercept is when y = 0 in an equation.
The x-intercept is the point where the line crosses the x-axis. It is found by setting y = 0 and solving the resulting equation. The y-intercept is the point where the line crosses the y-axis. It is found by setting x = 0 and solving the resulting equation.
Graph the equation 4x - y = 5.
Try to convert the equation 4x - y = 5 into the format
y = mx + b
4x - y = 5 can be converted into
y = 4x - 5
This means that m = 4 (the slope is 4) and b = -5 (the y-intercept is -5)
In the above graph, the slope is 4 and the y-intercept is -5.
In the above graph, the blue dot is the y-intercept at (0,-5).
The line slopes up at a rate of 4 up for every 1 across (slope of 4). It intersects lines at (1,-1) and (2,3).