# Thread: Equation of a line (two points)

1. ## Equation of a line (two points)

This is the question I am having trouble with:

Find the equation of the line joining each pair of given points- (-1,4) and (0,7).

This is my working:

Find the midpoint which is (1.5,3.5) then find the gradient which is 3. then write the equation y-3.5=3(x-1.5) then expand and rearange to form the equation 3x-y-1=0.

My answer is correct except for the -1 part. Could someone please show mw what I did wrong?

2. Originally Posted by Paulo1913
This is the question I am having trouble with:

Find the equation of the line joining each pair of given points- (-1,4) and (0,7).

This is my working:

Find the midpoint which is (1.5,3.5) then find the gradient which is 3. then write the equation y-3.5=3(x-1.5) then expand and rearange to form the equation 3x-y-1=0.

My answer is correct except for the -1 part. Could someone please show mw what I did wrong?
Your midpoint is quite wrong. In fact, the point you have found (how, I don't know) does not even lie on the line. If you plotted the two given points and joined them with a straight line you'd realise this immediately.

But why bother finding and using the midpoint??? You can use any point on the line, including (0, 7) which is the y-intercept. And you know y = mx + c .......

3. I'm sorry I don't quite understand what you mean

4. ## Check it out

If a and b are abcissa or ordinate of 2 points then mid point is defined as (a+b)/2 by doing so ur mid points should come (-0.5,5.5) so midpoint that u have calculated is wrong for sure. But there is no need of mid point.u can use any one of the given point.using midpoint will definetly give the answer but it will just be a unnecessary effort.

5. Originally Posted by Paulo1913
I'm sorry I don't quite understand what you mean
What don't you understand? Using the point (0, 7)? y = mx + c?

6. Originally Posted by Paulo1913
This is the question I am having trouble with:

Find the equation of the line joining each pair of given points- (-1,4) and (0,7).

This is my working:

Find the midpoint which is (1.5,3.5) then find the gradient which is 3. then write the equation y-3.5=3(x-1.5) then expand and rearange to form the equation 3x-y-1=0.

My answer is correct except for the -1 part. Could someone please show mw what I did wrong?
Find an equation of a line through (-1, 4) and (0,7)

1. Use the slope-intercept form of a linear equation:

$\displaystyle y=mx+b$ where m = slope(gradient) and b = y-intercept

$\displaystyle m=\frac{y_2-y_1}{x_2-x_1} = \frac{7-4}{0+1} = 3$

y-intercept = 7

Therefore, $\displaystyle \boxed{y=3x+7}$

2. Use the point-slope form of a linear equation:

$\displaystyle y-y_1=m(x-x_1)$ where m = slope(gradient) and $\displaystyle x_1, y_1)$ is any point on the line.

Therefore, using m = 3 and (-1, 4), we have

$\displaystyle \boxed{y-4=3(x+1)}$

Equations in (1.) and (2.) are equivalent.

7. ok I get it now. I have been rather slow lately lol