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Question 224640: Use patterns or a linear equation to complete the table
x y
1 -1
3 3
5 7
10 ?
50 ?
100 ?
Answer by drj(1380)   (Show Source):
You can put this solution on YOUR website! Use patterns or a linear equation to complete the table.
Based on the Steps below the equation is 
x y
1 y=2(1)-3=-1
3 3 use this point to find slope and equation of line (see below)
5 7 use this point to find slope and equation of line (see below)
10 ? y=2(10)-3=17
50 ? y=2(50)-3=100-3=97
Step 1. We are going to find the equation for this line in slope-intercept form given as y=mx+b where m is the slope and b is the y-intercept when x=0 or at point(0,b). Once we have this equation we can get the rest of the points.
Step 2. Based on your problem we will use two points to draw a line and these points are (3,3) and (5,7)
Step 3. The slope of the line m is given as
where for our example is x1=3, y1=3, x2=5 and y2=7 (think of  ). You can choose the points the other way around but be consistent with the x and y coordinates. You will get the same result.
Step 4. Substituting the above values in the slope equation gives
Step 5. The slope is calculated as 2 or m=-2
Step 6. Now use the slope equation of step 1 and choose one of the given points. I'll choose point (3,3). Letting y=y2 and x=x2 and substituting m=2 in the slope equation given as,
Step 7. Multiply both sides of equation by x-3 to get rid of denomination found on the right side of the equation
Step 8. Now simplify and put the above equation into slope-intercept form.
Add 3 to both sides of the equation
is in in slope-intercept form where m=2 and y-intercept=-3
Step 9. See if the other point (5,7) or x=5 and y=7 satisfies this equation
 So the point (5,7) satisfies the equation and is on the line. In other words, you can use the other point to check your work.
Note the above equation can be also be transform into standard form as
See graph below to check the above steps.
| Solved by pluggable solver: DESCRIBE a linear EQUATION: slope, intercepts, etc |
Equation  describes a sloping line. For any
equation ax+by+c = 0, slope is  .- X intercept is found by setting y to 0: ax+by=c becomes ax=c. that means that x = c/a. -3/-2 = 1.5.
- Y intercept is found by setting x to 0: the equation becomes by=c, and therefore y = c/b. Y intercept is -3/1 = -3.
- Slope is --2/1 = 2.
- Equation in slope-intercept form: y=2*x+-3.
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I hope the above steps were helpful.
And good luck in your studies!
For free Step-By-Step Videos on Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra or for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry.
Respectfully,
Dr J
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