SOLUTION: Not understanding equations and slopes. A line passing through (1,4) has a slope of m = 3. Another point on the same line is: a. (4,7) b. (4,4) c. (4,5)

Algebra ->  Linear-equations -> SOLUTION: Not understanding equations and slopes. A line passing through (1,4) has a slope of m = 3. Another point on the same line is: a. (4,7) b. (4,4) c. (4,5)       Log On


   

Question 147601: Not understanding equations and slopes.
A line passing through (1,4) has a slope of m = 3. Another point on the same line is: a. (4,7)
b. (4,4)
c. (4,5)
d. (1,7)
Please explain.
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
First let's find the equation of the line with a slope of 3 which goes through the point (1,4)


If you want to find the equation of line with a given a slope of 3 which goes through the point (1,4), you can simply use the point-slope formula to find the equation:


---Point-Slope Formula---
y-y%5B1%5D=m%28x-x%5B1%5D%29 where m is the slope, and is the given point

So lets use the Point-Slope Formula to find the equation of the line

y-4=%283%29%28x-1%29 Plug in m=3, x%5B1%5D=1, and y%5B1%5D=4 (these values are given)


y-4=3x%2B%283%29%28-1%29 Distribute 3

y-4=3x-3 Multiply 3 and -1 to get -3

y=3x-3%2B4 Add 4 to both sides to isolate y

y=3x%2B1 Combine like terms -3 and 4 to get 1
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Answer:


So the equation of the line with a slope of 3 which goes through the point (1,4) is y=3x%2B1



Notice how choice D) has the same x-coordinate as the given point. Since one x-value can only generate one y-value, this means that we can eliminate choice D)


Now also notice how the rest of the choices have an x-coordinate of 4. So let's plug in x=4 to find y


y=3x%2B1 Start with the given equation.


y=3%284%29%2B1 Plug in x=4.


y=12%2B1 Multiply 3 and 4 to get 12.


y=13 Combine like terms.


Since none of the choices have a y-coordinate of 13, this means that none of the choices are correct. So I would double check the problem.