I am having real trouble with the fractions in a slope intercept equation solving for x,!

Question

Y=5/4x +3       x=0          y=3

How do you solve for x step by step for the next ordered pair.

Answer 1

Salle, your equation y = (5/4)x + 3 is in slope-intercept form.    The slope or m is 5/4 and the y-intercept or b is 3.  You have already shown if x = 0, then y = 3.  This gives the ordered pair (0, 3) and this is the point on the graph of this equation where the line graphed crosses the y-axis.  You can find as many ordered pairs as you want (solutions) for this equation and you would begin by choosing a number for x.  Then we would use the equation to find the corresponding value of y.  You would prefer to choose numbers for x that do not give fraction values for y.  For example, x could equal 4 or 8 or -4 or -8.  These numbers will work best in the equation when solving for y because the denominator of the fraction 5/4 will cancel out.  If x is 4, we have y = (5/4)*4 + 3 and the 4's cancel out and we have y = (5/1)*1 + 3 and this gives y = 5 + 3 or 8.  This means the ordered pair (4, 8) is a solution of the equation and it is also another point on the line graphed by this equation.

Answer 2

There are probably two approaches you can take on this: 1. The slope is "rise divided by run". So, from a given point on the line, the slope goes up 5 units for every 4 units you move to the right. Using this approach, we can find another ordered pair based on the pair given (0,3): "Up 5" means we should add 5 to the y value, 3, which give us 8 "Over 4" means we should add 4 to the x value, 0, which gives us 4. So another point on the line would be (4,8). 2. You can pick an X value, plug it in, and solve for Y. Since the slope has a 4 in the denominator, I would probably choose something that was divisible by 4, to clear out that denominator - so let's pick X = 4. Plugging in, 4 Y = 5/4(4) + 3 = 5 + 3 = 8 So my ordered pair would be (4,8).

Answer 3

Hi, Salle.

It looks like you are off to a good start.

I am not sure, though, where you are headed. "Solving for x" means getting x alone on one side of the equation, but it will not give you an ordered pair. By the "next ordered pair" do you have specificied numbers to use for x? If not, it sounds like you are trying to determine points on the line, in preparation for graphing.

If you are graphing and just need to pick points, most often we pick 1, 0, and -1 for x. You're right though, that the fraction makes it a little trickier to graph that way. So I suggest using the number in the denominator of the fraction to make the problem a little easier.

We'll use 4 for x. Substituting 4 in for x:

y = 5/4(4) + 3

When multiplying by the fraction, remember that 4 is the same as 4/1.

y = 5/4 * 4/1 + 3

y = 20/4 + 3       (you could also factor out the 4 in the previous step if you want)

y= 5 + 3

y = 8

Multiplying a fraction by the number in the denominator gives you a whole number, so the point is easier to graph on the coordinate plane.

Hope this helps!