Understanding Linear Graphs
by Danielle
(Morton, Washington)
I have multiple word problems that are really giving me a hard time. I would really appreciate it if someone could help me.
1) The equations 3x+4y=8 and y=-3/4x+2 are equivalent. Which equation is easier to graph and why?
2) If the graph of the equation Ax+By=C is a horizontal line, what can you conclude about A? Why?
Karin from Algebra Class Says:
Hi Danielle,
I understand your frustration with word problems. These two questions are actually testing your knowledge of graphing linear equations. Your teacher wants to find out if you REALLY understand the concepts used to graph linear equations.
1. For the first question, you are given two equations:
3x + 4y = 8
y = 3/4x + 2
You know that the two equations are equivalent, but you want to know which one is easier to graph.
The only difference between the two equations is the form in which they are written.
3x + 4y = 8 is in standard form. Typically this form is a little more difficult to graph because you either have to find the x and y intercept (which in this case the x intercept is a fraction and really difficult to graph)or you would need to rewrite the equation in slope intercept form.
y = 3/4x + 2 is already written in slope intercept form and is always the easiest to graph. 2 is the y-intercept and this is your first point. Then you know that 3/4 is the slope, so you can find the second point. Once you have two point, you can draw your line.
Therefore, the second equation is the easiest to graph because it is written in slope intercept form.
This lesson will help you graph using slope intercept form:
https://www.algebra-class.com/slope-intercept-form.html
This lesson will help you graph using standard form:
https://www.algebra-class.com/y-intercept.html
Your second question gave you
Ax + By - C and told you that this is a horizontal line. What can you conclude about A.
In order to answer this question, you must understand that a horizontal line always has a slope of 0. The slope is always the coefficient of x in slope intercept form. If you rewrite this equation in slope intercept form, A would be the slope.
Therefore, A would have to be 0 if this were a horizontal line.
I hope that I've been able to help. If you continue to need help with this unit, check out the Graphing Equations unit. There are a lot of lessons there that might help you!
Best of luck,
Karin