There are two forms for expressing the equation of a line: point-slope form and standard form. Although they both describe the same line, it is important to know the difference between the two and how to convert from one to the other. This article will define both forms and give examples of how to switch them.
The most common way of expressing a line is in point-slope form, y=mx+b, where m is the slope and b is the y-intercept. This format tells you everything you need to know to reconstruct the line in a graph, so it is very useful for that purpose.
Standard form equations are expressed as Ax+By=C, as many equations are written. As you will see with an example, the standard and point-slope forms both refer to the same line. The point-slope form makes it easier to graph, which is why it is a good idea to know how to convert one form to the other.
Convert 3x+4y=24 into point-slope form.
To convert this standard form equation into point-slope form, you want all the y on one side and all x and constants on the other. Subtract 3x from both sides and you get 4y=24-3x. Divide both sides by 4 to get y=-3/4x+6. What this point-slope equation tells us is that we have a line with a slope of -3/4 with a y-intercept of 6. By marking the point (0,6) on your graph, move to the left 3 and up 4, you have your second point and can make your line.
Convert y=-3/4x+6 into standard form.
To show you that these equations represent the same line, let's work backwards with the point-slope form equation we ended with in the first example. To convert to standard form, we want all the x and y on one side and all the constants on the other. Add 3/4x to both sides and we get 3/4x+y=6. Standard form equations are best not represented with fractions, so multiply by 4 to get rid of the 3/4 and we get 3x+4y=24. To graph this line, simply put values into either x or y and solve for the other to get your points. If x=0, you have 3*0+4y=24, then 4y=24, y=6. Put in 0 for y and you get 3x=24, x=8. Plot these two points (0,6) and (8,0) and you have your line.
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