How do you plot the graph of the equation I forgot can somebody please help me?

Question

1. Plot the graph of the equations 3x - 8y = 5 and 4x - 2y = 11 and interpret the result.

2. Plot the graph of the equations 4x - 6y = 2 and 2x - 3y = 1 and interpret the result.

3. Plot the graph of the equations 10x - 4y = 3 and 5x - 2y = 6 and interpret the result.

Answer 1

These are equations for pairs of lines.  Basically there are 3 possibilities -- parallel lines, lines that intersect at a point, and lines that are identical.  

So you need to graph the lines and see which case is which (hint: you have one of each).

To plot the graph of a line, there are at least two things you can do.

Method 1: convert to slope-intercept form y = mx + b

This is a line with slope m, and y-intercept b -- to draw it you need a line that has a height of b where it crosses the y-axis (x = 0), and goes up by an amount m every time x increases by 1 (down by |m| if m is negative).

To convert to slope-intercept form, first subtract the "x" term from both sides of the equation, and then divide by the coefficient in front of the y.

I'll do one example:

3x - 8y = 5 is the same as:

-8y = -3x + 5, (subtracting 3x from each side), which is the same as:

y = (3/8)x - (5/8) (dividing each side by -8)

so draw the graph of the line that passes thru (0, -5/8) and goes up by 3/8 for each unit step to the right, down by 3/8 for each unit step to the left

Method 2: plug in some point (2 is enough for each line, but a 3rd will help check for errors).  For example, plug in x = 0 and solve for y.  Then plug in y = 0 and solve for x.  So in the first line, you know that (0, -5/8) is a point on the line, as well as (5/3,0).  plot those 2 points, take a straight-edge, and connect them, and you get the line.

Now, in the case of parallel lines, the slope will be the same but the y-intercept different.  In the case of intersecting lines, if you draw the graph you should be able to see where they intersect -- you can try to find the exact point by plugging in to the 2 equations, a good guess from the graph.

Answer 2

Hi there,

Here's how to graph a line:

3x - 8y = 5.....get y by itself on one side

3x - 5 = 8y.....divide by 8 to get y alone.

(3x/8) - (5/8) = y...look at it in y = mx + b

m = 3/8 ... y intercept b = -5/8.

To graph it, start with the point (0, -5/8).  Then graph points that are up 3 and over 8.  Connect the dots.

Now if the two equations have the same slope m, the lines are parallel.  If the slopes are "negative reciprocals", the lines are perpendicular.  m1 = 3/8, and m2 = -8/3.  Otherwise the lines cross somewhere else.  

They intersect at the solution of the two equations, using elimination or substitution, OR the point that the line graphs intersect.