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

2 Answers | Add Yours

justaguide's profile pic

justaguide | College Teacher | (Level 2) Distinguished Educator

Posted on

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).

giorgiana1976's profile pic

giorgiana1976 | College Teacher | (Level 3) Valedictorian

Posted on

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.

We’ve answered 318,957 questions. We can answer yours, too.

Ask a question