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

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) (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

where for our example is x1=1, y1=202, x2=4 and y2=382 (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 3. Substituting the above values in the slope equation gives

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,

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

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

Add 202 to both sides of the equation

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

{{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

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. 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) (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

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