SOLUTION: what is the y intercept of the points (1, 202) and (4, 382)?

Algebra ->  Coordinate Systems and Linear Equations  -> Lessons -> SOLUTION: what is the y intercept of the points (1, 202) and (4, 382)?      Log On


   

Question 215585: what is the y intercept of the points (1, 202) and (4, 382)?
Found 2 solutions by drj, solver91311:
Answer by drj(1380) About Me  (Show Source):
You can put this solution on YOUR website!
What is the y intercept of the points (1, 202) and (4, 382)?

Step 1. We need to find an equation in slope intercept form given as y=mx+b where m is the slope and b is the y-intercept at point (0,b).

Step 2. The slope of the line m is given as

+m=%28y2-y1%29%2F%28x2-x1%29

where for our example is x1=1, y1=202, x2=4 and y2=382 (think of slope=rise%2Frun). 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 3. Substituting the above values in the slope equation gives

m=%28382-202%29%2F%284-1%29

m=180%2F3

m=60

Step 4. The slope is calculated as 60 or m=60.

Step 5. Now use the slope equation of step 1 and choose one of the given points. I'll choose point (1,202). Letting y=y2 and x=x2 and substituting m=60 in the slope equation given as,

+m=%28y2-y1%29%2F%28x2-x1%29


+60=%28y-202%29%2F%28x-1%29

+60=%28y-202%29%2F%28x-1%29

Step 6. Multiply both sides of equation by x-1 to get rid of denomination found on the right side of the equation


+60%28x-1%29=%28x-1%29%28y-202%29%2F%28x-1%29


+60x-60=y-202


Step 7. Now simplify and put the above equation into slope-intercept form.

60x-60=y-202

Add 202 to both sides of the equation

60x-60%2B202=y-202%2B202

60x%2B142=y

y=60x%2B142 ANSWER in slope-intercept form. m=60 and y-intercept=142

Step 8. See if the other point (4, 382) or x=4 and y=382 satisfies this equation

y=60x%2B142

382=60%2A4%2B142

{{382=382}}} So the point (4,382) satisfies the equation and is on the line. In other words, you can use the other point to check your work.

Note: above equation can be also be transform into standard form as

-60x%2By=142

See graph below to check the above steps.

Solved by pluggable solver: DESCRIBE a linear EQUATION: slope, intercepts, etc
Equation -60+x+%2B+1+y+=+142 describes a sloping line. For any
equation ax+by+c = 0, slope is -a%2Fb+=+--60%2F1.
  • X intercept is found by setting y to 0: ax+by=c becomes ax=c. that means that x = c/a. 142/-60 = -2.36666666666667.
  • Y intercept is found by setting x to 0: the equation becomes by=c, and therefore y = c/b. Y intercept is 142/1 = 142.
  • Slope is --60/1 = 60.
  • Equation in slope-intercept form: y=60*x+142.



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

Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!


The two given points do not have a -intercept. The line that passes through the two given points does have a -intercept however. Presuming that is what you really meant to ask, proceed as follows:

Use the two-point form of the equation of a line:



where and are the ordered pairs describing the given points.

Make the appropriate substitutions of coordinate values:



Giving you AN equation for the desired line. Next simplify and solve for putting your equation into slope-intercept form, namely . The -intercept is then the point .

John