Most cars won’t be able to run for more than 250,000 miles, so how much longer will your car live? Linear Equations are the most basic kind of algebraic function and can help you answer questions exactly like this. Learn about what they look like, how they come up in your life and why they are powerful tools.
Defining a Linear Equation
This lesson is on what a linear equation is. And the answer to that question is essentially a linear equation is any pattern of numbers that is increasing or decreasing by the same amount every step of the way. This means that the only two things that we need to define a linear equation are where the pattern begins and what that pattern moves by. What that leaves us with is the slope-intercept form of the linear equation, y = mx + b, where the m value is the slope, and the b value is the y-intercept.
Building a Linear Equation
Some examples of linear equations in slope-intercept form: You could have y = 2x + 1; you could have y = -3x; and you could have y = (2/3)x – 6. In each equation, the number in front of the x represents the slope or the number that it’s moving by. The number on the end represents where it begins, or the y-intercept. If there is no number after the x, that implies that the y-intercept is zero.
What’s the point? Why do I care about a linear equation? Well, linear equations are the most common patterns of numbers we see, and they can be used to describe all sorts of situations you see around you.
One example has to do with the first car I bought. As soon as I turned 16, my parents helped me buy a used car. When I got my car it had 27,000 miles on it, and I’ve owned it for a while now. Every year, I drive it about 12,000 more miles. What we end up with is a linear equation to represent the situation that looks like y = 12,000x + 27,000, because I drive it 12,000 more miles every year, and that’s how much the pattern moves by. And the pattern began at 27,000 miles when I first bought the car. So, after year one, it had 39,000; after year two, it had 51,000; and after year three, it had 63,000. And so on.
Solved Example on Linear Equation:
There were a hundred schools in a town. Of these, the number of schools having a playground was 30, and these schools had neither a library nor a laboratory. The number of schools having a laboratory alone was twice the number of those having a library only. The number of schools having a laboratory as well as a library was one fourth the number of those having a laboratory alone. The number of schools having either a laboratory or a library or both was 35. What was the ratio of schools having a laboratory to those having a library?
(a) 1 : 2
(b) 5 : 3
(c) 2 : 1
(d) 2 : 3
Total number of schools = 100
Schools with Playgrounds = 30
Number of schools with library alone = X
Number of schools with laboratory alone = 2X
Number of schools with library and laboratory = 1/4 * 2X = X/2
Number of schools having either a library or laboratory or both = 35
— > X + 2X + X/2 = 35
— > X = 10
Schools having Laboratory = 2 x 10 + 10/2 = 25
Schools having Library = 10 + 5 = 15
Required ration = 25/15 = 5:3
In this post, we have defined Linear Equation and helped you in building a Linear Equation with giving a proper detailed example.
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