What are the charateristics of the graph of the line: 4x – 3y – 24 = 0
The equation of the line that has to be graphed and its characteristics determined is 4x - 3y - 24 = 0
This can be written in the form x/a + y/b = 1 where a is the x-intercept and b is the y-intercept.
4x - 3y - 24 = 0
=> 4x - 3y = 24
=> x/6 - y/8 = 1
The x-intercept is (6, 0) and the y-intercept is (0, -8).
To determine the slope of the line we write it in the form y = mx + c, where m is the slope.
4x - 3y - 24 = 0
=> -3y = -4x + 24
=> y = (4/3)x - 8
The slope of the line is (4/3).
The form of the equation of the line you,ve provided is the standard form.
We'll put this equation in the slope intercept form. For this reason, we'll isolate -3y to the left side shifting the rest of expression to the right side:
-3y = -4x + 24
We'll divide by -3:
y = 4x/3 - 24/3
y = 4x/3 - 8
Comparing both forms:
y = mx + b, where m is the slope of the line and b is y intercept, we'll get:
m = 4/3 and y = -8
m = tan a => a = arctan m, where a is the angle made by the line to x axis.
Now, we'll determine the intrcepting point of the line with x and y axis.
When the line is intercepting x axis, y coordinate is 0.
4x/3 - 8 = 0
4x/3 = 8
4x = 24
x = 6
The intrercepting point with x axis is: (6,0).
It is no need to determine the intercepting point with y axis, because we already found it.
The intercepting point with y axis is (0,8).
Therefore, the characteristics of the given line are the intercepting points with x and y axis and the angle made by the line to x axis, which may be found when we know the value of the slope: x axis intercept (6,0) ; y axis intercept (0,8) and the slope m=4/3.