SOLUTION: HI!! please help me with this Find the equation of a line with the slope of 2/3 that passes through the points (4,-1) ps.the answer is 2/3x-11/3 but i dont know how to get

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Question 109124: HI!!
please help me with this
Find the equation of a line with the slope of 2/3 that passes through the points (4,-1)
ps.the answer is 2/3x-11/3
but i dont know how to get it

Found 2 solutions by MathLover1, jim_thompson5910:
Answer by MathLover1(20850)   (Show Source): You can put this solution on YOUR website!

Solved by pluggable solver: FIND a line by slope and one point

What we know about the line whose equation we are trying to find out:

  • it goes through point (4, -1)

  • it has a slope of 0.666666666666667



First, let's draw a diagram of the coordinate system with point (4, -1) plotted with a little blue dot:



Write this down: the formula for the equation, given point and intercept a, is

(see a paragraph below explaining why this formula is correct)

Given that a=0.666666666666667, and , we have the equation of the line:



Explanation: Why did we use formula ? Explanation goes here. We are trying to find equation y=ax+b. The value of slope (a) is already given to us. We need to find b. If a point (, ) lies on the line, it means that it satisfies the equation of the line. So, our equation holds for (, ): Here, we know a, , and , and do not know b. It is easy to find out: . So, then, the equation of the line is: .

Here's the graph:
Answer by jim_thompson5910(35256)   (Show Source): You can put this solution on YOUR website!

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


---Point-Slope Formula---
where is the slope, and is the given point

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

Plug in , , and (these values are given)


Rewrite as


Distribute

Multiply and to get

Subtract 1 from both sides to isolate y

Combine like terms and to get (note: if you need help with combining fractions, check out this solver)


------------------------------------------------------------------------------------------------------------
Answer:


So the equation of the line with a slope of which goes through the point (,) is:

which is now in form where the slope is and the y-intercept is

Notice if we graph the equation and plot the point (,), we get (note: if you need help with graphing, check out this solver)

Graph of through the point (,)
and we can see that the point lies on the line. Since we know the equation has a slope of and goes through the point (,), this verifies our answer.
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