Equation of a line through 2 points

[Guest]

Find the equation of a line through point(4, 5) intersecting OY at point y = 2

[Guest]

So we have to find the equation of a line through two points:
the first point: (4, 5)
the second point: (0, 2)

so lets the equation is y=ax + b
then we have:
5 = a*4 + b
0 = a*2 + b => a = -b/2

5 = -2b +b
b = -5
a=2.5
y=2.5x - 5

[Guest]

I think there is a formula for a line slope through two points.

[Math Tutor]

Yes there is a formula for finding equation of a line through two points.

[tex]\frac{y - y_1}{x - x_1} = \frac{y_2 - y_1}{x_2 - x_1}[/tex]

where [tex]x_1 = 4[/tex], [tex]y_1 = 5[/tex] and [tex]x_2 = 0[/tex], [tex]y_2 = 2[/tex]

[Guest]

The eq of line is y=mx+b and As we know that m=y2-y1/x2-x1 which gives us the value of m that is 3/4 and the value of b is 2 so your answer will be y=3/4x+2.

[salakh74]

As we have two points.First find the slope by applying the formula..then we have slope point formula to find the equation of straight line

[Alicelewis11]

To find Equation of a line through 2 points, for this purpose you can use this formula.
y-y1 = m(x-x1).....

[leesajohnson]

Using this formula you can solve this question.

y-y1/x-x1 = y2-y1/x2-x1

where given x1=4 and y1=5
x2=0 and y2=2

[Guest]

Are there people in misery here.......
If we go back to original question..........

So we have to find the equation of a line through two points:
the first point: (4, 5)
the second point: (0, 2)

The equation is of the form y = mx + c

You should spot from the second point: (0, 2) that when x=0 then y=2 ...So c = 2.

m = (y1 - y2) / (x1 - x2)

m = (5 - 2) / (4 - 0)

m = 3/4 = 0.75

5 = 0.75*4 +c

c = 2 as shown above

Equation is ... y = 0.75x + 2

[HallsofIvy]

There are many different ways to find the equation of a line through two points! The first and last post both gave what is probably the simplest: any (non-vertical) line can be written in the form y= mx+ b. Setting x and y equal to the x and y components of the two points (here (4, 5) and (0, 2)) give the two equations 5= 4m+ b and 2= 4(0)+ b= b. Those two equations can be solved for m and b. From the second equation, b= 2 so the first equation becomes 5= 4m+ 2 so 4m= 5- 2= 3 and m= 3/5. y= (3/4)x+ 2.

Or we can first calculate the slope, m. The two points are [tex](x_1, y_1)= (4, 5)[/tex] and [tex](x_2, y_2)= (0, 2)[/tex] so the slope is [tex]\frac{y_2- y_1}{x_2- x_1}= \frac{2- 5}{0- 4}= \frac{-3}{-4}= \frac{3}{4}[/tex]. Knowing that the "y intercept" is 2 tell is that y= m(0)+ b= b= 2 so again we get y= (3/4)x+ 2.

Or, we can use geometric fact that, since the graph is a straight line, three points on the line, (4, 5), (0, 2), and the "generic" (x, y), together with horizontal and vertical lines at each point give two similar right triangle so that the ratios of vertcal lenths, y- 5 and 2- 5, to horizontal lengths,, x- 4 and 0- 4, are the same : [tex]\frac{y- 5}{x- 4}= \frac{2- 5}{0- 4}= \frac{3}{5}[/tex]. Multiply both sides by x- 4 to get [tex]y- 5= \frac{3}{4}(x- 4)= \frac{3}{4}x- 3[/tex]. Add 5 to both sides to get, yet again, [tex]y= \frac{3}{4}x+ 2[/tex].

[Guest]

yes there is formula to find slope of line through two points
i.e. m = (y2- y1)/(x2 - x1)

where m is the slope of line and (x1,x2) and (y1,y2) are two points.

visit https://mathemerize.com/find-slope-of-line/ to learn more concepts of slope of line.

[Guest]

Using this formula you can solve this question.

y-y1/x-x1 = y2-y1/x2-x1

where given x1=4 and y1=5
x2=0 and y2=2

Unfortunately this is wrong!
What you should use is (y-y1)/(x-x1)= (y2-y1)/(x2-x1)
You need parentheses.

[Raiden Mitchell]

There are many different ways to find the equation of a line through two points! The first and last post both gave what is probably the simplest: any (non-vertical) line can be written in the form y= mx+ b. Setting x and y equal to the x and y components of the two points (here (4, 5) and (0, 2)) give the two equations 5= 4m+ b and 2= 4(0)+ b= b. Those two equations can be solved for m and b. From the second equation, b= 2 so the first equation becomes 5= 4m+ 2 so 4m= 5- 2= 3 and m= 3/5. y= (3/4)x+ 2.

Or we can first calculate the slope, m. The two points are [tex](x_1, y_1)= (4, 5)[/tex] and [tex](x_2, y_2)= (0, 2)[/tex] so the slope is [tex]\frac{y_2- y_1}{x_2- x_1}= \frac{2- 5}{0- 4}= \frac{-3}{-4}= \frac{3}{4}[/tex]. Knowing that the "y intercept" is 2 tell is that y= m(0)+ b= b= 2 so again we get y= (3/4)x+ 2.

Or, we can use geometric fact that, since the graph is a straight line, three points on the line, (4, 5), (0, 2), and the "generic" (x, y), together with horizontal and vertical lines at each point give two similar right triangle so that the ratios of vertcal lenths, y- 5 and 2- 5, to horizontal lengths,, x- 4 and 0- 4, are the same : [tex]\frac{y- 5}{x- 4}= \frac{2- 5}{0- 4}= \frac{3}{5}[/tex]. Multiply both sides by x- 4 to get [tex]y- 5= \frac{3}{4}(x- 4)= \frac{3}{4}x- 3[/tex]. Add 5 to both sides to get, yet again, [tex]y= \frac{3}{4}x+ 2[/tex].

Thank you very much for the recommendation and the fact that you described in detail the formulas with which you can find the equation of a straight line passing through 2 points. Using the geometric factor in this case will also help speed up the process of finding the right answer.

[Guest]

The eq of line is y=mx+b and As we know that m=y2-y1/x2-x1 which gives us the value of m that is 3/4 and the value of b is 2 so your answer will be y=3/4x+2.

m= (y2- y1)/(x2- x1)

And it would be better to write y= (3/4)x+ 2