Shannon P. answered • 07/18/14
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Hello there, Jennifer! I hope I can help. If my explanation does not satisfactorily answer your problem, simply let me know, here. Also, if I explain something that you already know, please forgive me.
Let's start with the Slope-Intercept formula, which is y=mx+b. I'm sure you already know that m=slope, and b=the point where the line crosses the y-axis (the y-intercept). So, it's easy to write these formulas all day long in Slope-Intercept form if you know the two aforementioned values. It gets tricky, however, if you have to figure out either one of those values.
Slope-Intercept is nothing more than a way to describe a straight line on a graph. Line formulas and equations serve this purpose: they are simply sentences, if you will, that let us put in values, and get other values out. Because a line on a graph has infinite points on a Cartesian Plane, we have to have a way to describe that line that allows for us to find points, know which way it goes, and see how steep it is, without having to input ordered pairs ad infinitum. There are generally 3 standard formulas for describing lines, and basically each one is going to give you the same information (the line). You know Slope-Intercept. The other 2 are Point-Slope (y-y1)=m(x-x1), and the General Form (ax+by=c), where c is the y-intercept. Each formula is derived from the same concept, and simply serve the purpose of making it easier for the mathematician to glean needed information as efficiently as possible. You can simply choose which formula to use based on what information you are already given; what you already know, and what you need to find out will determine which of the 3 formulas you want to use. Basically, if you have slope and one point, you'll use Slope-Intercept. If you have two points, you'll use Point-Slope. Etc, etc.
In your problem, you need to ultimately describe a line using the Slope-Intercept form. You already know slope, so thus far you can say y=4x+b. That was easy enough, but what value do you use for b?
Because we know one of the ordered pairs, we can plug in the x and y values from that and solve for b. Things get real easy, after that. So, in your problem, we know the slope is 4, and we have one point where x=6, and y=-1. Let's just plug in those values. y=mx+b => -1=4(6)+b => -1=24+b => b=-25. Because we knew an x and y value, along with the slope (m), it was easy for us to figure out the y-intercept (b). And now, all we have to do is write the formula using our found values. y=4x-25.
Don't forget that with equations, if you're ever unsure you have the right answer, you can always test it. For your problem, we can test if (6,-1) really does show up in our finished formula. For example, plug in y, but not x, and see if you get 6 for x. y=4x-25 => -1=4x-25 => 4x=24 => x=6. And, you can do the same thing plugging in x and solving for y.
Let's start with the Slope-Intercept formula, which is y=mx+b. I'm sure you already know that m=slope, and b=the point where the line crosses the y-axis (the y-intercept). So, it's easy to write these formulas all day long in Slope-Intercept form if you know the two aforementioned values. It gets tricky, however, if you have to figure out either one of those values.
Slope-Intercept is nothing more than a way to describe a straight line on a graph. Line formulas and equations serve this purpose: they are simply sentences, if you will, that let us put in values, and get other values out. Because a line on a graph has infinite points on a Cartesian Plane, we have to have a way to describe that line that allows for us to find points, know which way it goes, and see how steep it is, without having to input ordered pairs ad infinitum. There are generally 3 standard formulas for describing lines, and basically each one is going to give you the same information (the line). You know Slope-Intercept. The other 2 are Point-Slope (y-y1)=m(x-x1), and the General Form (ax+by=c), where c is the y-intercept. Each formula is derived from the same concept, and simply serve the purpose of making it easier for the mathematician to glean needed information as efficiently as possible. You can simply choose which formula to use based on what information you are already given; what you already know, and what you need to find out will determine which of the 3 formulas you want to use. Basically, if you have slope and one point, you'll use Slope-Intercept. If you have two points, you'll use Point-Slope. Etc, etc.
In your problem, you need to ultimately describe a line using the Slope-Intercept form. You already know slope, so thus far you can say y=4x+b. That was easy enough, but what value do you use for b?
Because we know one of the ordered pairs, we can plug in the x and y values from that and solve for b. Things get real easy, after that. So, in your problem, we know the slope is 4, and we have one point where x=6, and y=-1. Let's just plug in those values. y=mx+b => -1=4(6)+b => -1=24+b => b=-25. Because we knew an x and y value, along with the slope (m), it was easy for us to figure out the y-intercept (b). And now, all we have to do is write the formula using our found values. y=4x-25.
Don't forget that with equations, if you're ever unsure you have the right answer, you can always test it. For your problem, we can test if (6,-1) really does show up in our finished formula. For example, plug in y, but not x, and see if you get 6 for x. y=4x-25 => -1=4x-25 => 4x=24 => x=6. And, you can do the same thing plugging in x and solving for y.
I hope this helps you to understand better these line formulas. If you're so inclined, also check out this page: http://www.purplemath.com/modules/strtlneq.htm. I love Purplemath, as they are great at explaining mathematical concepts in an easy-to-understand way.
Good luck, Jennifer!
Jahlen P.
03/07/15