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# Comparing linear functions: equation vs. graph

Sal is given the formula of a linear function and the graph of another, and is asked to determine which function increases faster. Created by Sal Khan.

## Want to join the conversation?

• If ax + by + c = 0 is a linear equation in two variables. Is x + 0y + 7 = 0 a linear equation in 2 variables?
• Yes, the second example is also a linear equation in two variables. Similarly, `0x + 0y + 0z = 0` is a linear equation in three variables, albeit one with an infinite number of solutions.

Having a coefficient of 0 doesn't mean that the variable goes away. It still exists, it is simply irrelevant and can take on any value without affecting the validity of the equation.
• my teacher wants me to (sooner or later) describe a linear function. how should I do that?
• Zachary,
Lets break up the word. Linear means something that makes a line (pretty simple,) and a function is a set of coordinates or points on a graph that have only one x value to every y value. So basically, a linear function does not curve, but goes in a strait line on a graph. If it curves, this is called a non-linear function.
I hope this helped!
• At , how did Sal plot a "g" out of nowhere?
• He wasn't plotting a point named "g". He was showing that the line on the graph is the function "g(x)"; this is stated in the text of the exercise.
• why is math like this?
• At , if both are increasing then don't the negatives cancel out and become positive?
• You are comparing the slopes, not multiplying the slopes.
Both lines are negative, so both lines slant down from left to right. The slope of line F is decreasing faster because its slope is more negative than the slope of line G.
Hope this helps.
• The way this was laid out confused me. I thought that the equation was referring to the graph as well, and I just assumed that they were representing the same thing until we actually broke down the slope of the graph.. The whole 'g is a function of x' thing is a bit confusing, and I wish that we went over that more in the functions lesson.

Hopefully we will touch on that in the next few videos.
• is y=1/x - 7 a linear function
(1 vote)
• No, it isn't. Anything that has the formula y=m/x + q is a hyperbola function.
• Graph the linear function with the equation y=1/2x+3
• Your equation is in slope-intercept form already so graphing it is pretty easy.
Just looking at the equation, you can tell it crosses the y-axis at (0,3) so plot that point.
Now use the slope (1/2) to find another point. Your slope tells you to go up one and over to the right 2 to get to the next point. Since it's a positive number, your line will slope upwards.
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|f you aren't comfortable with the slop-intercept form yet, I suggest: