Algebra

Question

how do you determine an equation in slope-intercept form? What can of graph would this come to be?

Answer

&nbsp;Hi,<BR>&nbsp; Slope-intercept is normally a straight-line graph.&nbsp; The equation would be of the form y = ax + b.&nbsp; The y in the equation is the verticle scale.&nbsp; The x (which is multiplied by the&nbsp;constant "a") which lays along the horizonal axis is the varible or input that you are asked to compute an answer for y.&nbsp; Given a value for x, you multiple it by the value "a" then add the value of b.&nbsp; If you were to think of x as distance and y as height, the further you walk away (in a positive direction) the higher the value of y becomes.&nbsp; Y could also become lower if the value of "a" is preceded by a negative sign.&nbsp;&nbsp;<BR>&nbsp; That's some of the background for a linear equation (the y = ax + b).&nbsp; Suppose x were to equal zero.&nbsp; Then the term "ax" would also become zero (and disappear from the equation) leaving just the value for b.&nbsp; The b value is therefore the point where the line intercepts the y-axis when the x-axis value is zero.&nbsp; The value of b could be positive or negative.&nbsp; You only have to look at a graph to see where the line crosses the y-axis and you have the value for the slope intercept.&nbsp;&nbsp;You are half-way done when you figure this value out.&nbsp; Actually, there's not much to figure out, you just look at the picture and note the number.&nbsp; <BR>&nbsp; The "a" in the equation represents the slope of the line.&nbsp; Sometimes the slope (the "a" value)&nbsp;is just a number&nbsp;and other times it could be a fraction.&nbsp; If the slope is a plain number, pretend it is divided by the number one and that will make it a fraction.&nbsp; The numerator (the number on the top of the fraction) represents the horizontal rise (or fall if there is a negative sign) and the denominator (the number on the bottom) represents the distance run along a horizontal axis.&nbsp;&nbsp;<BR>&nbsp; Sometime books will suggest you note where the line crosses the x-axis and use that value for the denominator value in the fraction representing "a" and use the value for the y-intercept in&nbsp;the numerator.&nbsp;&nbsp;&nbsp; I don't always use that method but look for what appears to be a right triangle and count the length of each of the side of the triangle.&nbsp;&nbsp; The horizontal value goes in the denominator and the verticle value goes in the numerator.&nbsp; In any case, most fractions will need to be reduced or you should check to see if the fraction is reducible.&nbsp; The sign of the value&nbsp;for&nbsp;"a" depend on whether or not the line slopes down to the right or goes up to the right.&nbsp; Negative in the first case and positive in the second.<BR>&nbsp; At this point, you're done except for the recording of the information.&nbsp; Write down "y =" then the reduced fraction followed by X then the value of y observed above (where you were half-way done).&nbsp;&nbsp;Now you are done.&nbsp;&nbsp;<BR>&nbsp; Let's check our work.&nbsp;&nbsp;Here are the rules:<BR>1.&nbsp;If the line intercepts the y-axis below the horizontal scale, b is a negative number.<BR>2.&nbsp;If the line slopes (goes) up to the right, "a" is a positive number.<BR>3. If the line slopes down to the right, "a" is a negative number.<BR><BR>&nbsp; Hope this helps.&nbsp; Sorry it has to be so long...but I wanted to make sure you knew what I was talking about.&nbsp; http://vrd.askvrd.org/services/answerschema.xml