Quote from DianaJH
Hi, thanks for the reply!
Happy to help
Quote from DianaJH
It does have the line in the graph, but do you know what? I have forgotten this stuff! I aced both algebra classes and can't remember this for anything. I am not even understanding what you typed except that you did get the answer of 5!
OK, let's see if I can clarify what I posted.
The original information you posted gave us a point (x, y) of (1.5, -3) which I plugged into the equation y = mx + b to get:
-3 = m(1.5) + b.
You also provided the other point on the line. X = 4 from the original question and Y = 5 from the answer in your book which I once again plugged into the equation to get:
5 = m(4) + b
At this point we know neither the slope of the line (m), nor the y-intercept (b). So the first thing I did was determine the slope of the line (m) by calculating the rise of line over the run of the line defined as:
rise / run = (Change in Y) / (Change in X) = (Y2 - Y1) / (X2 - X1) =
(5 - (-3)) / (4 - 1.5) = 8 / 2.5 = 3.2
So if we plug in the newly calculated slope of the line (m) to our two equations earlier we get:
-3 = 3.2(1.5) + b
5 = 3.2(4) + b
The only thing left to determine is the y-intercept (b). So using the following formula: y - y1 = m(x - x1) with the first point provided from the problem (1.5, -3) we end up with:
y - (-3) = 3.2(x - 1.5)
Then we solve and reduce:
y + 3 = 3.2x - 4.8
y = 3.2x - 7.8
So to find the y-intercept we set x = 0 which gives us:
y = 3.2(0) - 7.8
which reduces to:
y = -7.8
So now we know:
y = 3.2x - 7.8 will provide us with y for any given x value.
By rearranging the equation we can find x for any given y by using:
x = (y + 7.8) / 3.2
Given all the previous steps, by plugging in the supplied value where x = 4, we can solve for y.
y = 3.2(4) - 7.8
y = 12.8 - 7.8
y = 5
And from your book, you know that the correct answer was indeed 5.
Hope that helps to bring it all back to you.
Best of luck on the exam and getting into your preferred nursing program.