What are the charateristics of the graph of the line: 4x – 3y – 24 = 0

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.