Find a missing coordinate using slope calculator with fractions

Usually, we use the slope formula to find the slope of a line when we know two points on the line. But if we already know the slope of a line, we can use the slope formula to find a missing coordinate of a point on the line.

Here's the slope formula we'll be using: 

ExampleFind x if the line through the points (6, x) and (1, -5) has a slope of 2. Since the slope of the line is 2, we'll replace the m in our slope equation with 2. The two points will give us the numbers and variable that will replace the subscripted variables in the slope equation.

Be careful here! Did you notice that the x in the first point is really the y-coordinate of that point? Now we'll use the slope formula to find the value of x, the missing y-coordinate.

-10 = -5 - x

-5 = -x

-1(-5) = -1(-x)

5 = x

x = 5

OK, the answer is x = 5, but what does the answer mean? It means that if we substitute 5 for the missing coordinate in the first point, the slope of the line between the two points will be equal to 2. If you want to check this answer, just use the slope formula to find the slope of the line between (6,5) and (1,-5). If the slope of this line is 2, you know that your answer of x=5 is correct.

Please disable adblock in order to continue browsing our website.

Unfortunately, in the last year, adblock has now begun disabling almost all images from loading on our site, which has lead to mathwarehouse becoming unusable for adlbock users.

Example 1 :

The slope of a line is 3/2 and the line contains the points (5, 9) and (3, a). What is the value of a ?

Solution :

Formula to find the slope of a line when two points are given : 

m  =  (y2 - y1) / (x2 - x1)

Given : Slope of the line is 3/2. 

Then, 

(y2 - y1) / (x2 - x1)  =  3/2

Substitute (x1, y1) = (5, 9) and (x2, y2) = (3, a). 

(a - 9) / (3 - 5)  =  3/2

(a - 9) / (-2)  =  3/2

Multiply each side by (-2).

a - 9  =  -3

Add 9 to each side. 

a  =  6

Example 2 :

The slope of a line is -2 and the line contains the points (7 , 4) and (x, 12). What is the value of x ? 

Solution :

Formula to find the slope of a line when two points are given : 

m  =  (y2 - y1) / (x2 - x1)

Given : Slope of the line is -2. 

Then, 

(y2 - y1) / (x2 - x1)  =  -2

Substitute (x1, y1) = (7, 4) and (x2, y2) = (x, 12). 

(12 - 4) / (x - 7)  =  -2

8 / (x - 7)  =  -2

Take reciprocal on each side. 

(x - 7) / 8  =  -1/2

Multiply each side by 8.

x - 7  =  -4

Add 7 to each side. 

x  =  3

Example 3 :

The slope of a line is 2/t and the line contains the points (-2 ,4) and (-6, 10). What is the value of t?

Solution :

Formula to find the slope of a line when two points are given : 

m  =  (y2 - y1) / (x2 - x1)

Given : Slope of the line is 2/t. 

Then, 

(y2 - y1) / (x2 - x1)  =  2/t

Substitute (x1, y1) = (-2, 4) and (x2, y2) = (-6, 10). 

(10 - 4) / (-6 + 2)  =  2/t

6 / (-4)  =  2/t

-3/2  =  2/t

Take reciprocal on each side. 

-2/3  =  t/2

Multiply each side by 2.

-4/3  =  t

Example 4 :

The line through the points (-2, a) and (9, 3) has slope -1/2. Find the value of a.

Solution :

Formula to find the slope of a line when two points are given : 

m  =  (y2 - y1) / (x2 - x1)

Given : Slope of the line is -1/2. 

Then, 

(y2 - y1) / (x2 - x1)  =  2/t

Substitute (x1, y1) = (-2, a) and (x2, y2) = (9, 3). 

(3 - a) / (9 + 2)  =  -1/2

(3 - a) / 11  =  -1/2

Multiply each side by 11.

3 - a  =  -11/2

Subtract 3 from each side.

-a  =  -11/2 - 3

-a  =  -11/2 - 6/2

-a  =  (-11 - 6) / 2

-a  =  -17/2

Multiply each side by (-1).

a  =  17/2

Example 5 :

The line through the points (-2, 6) and (4, 8) is perpendicular to the line through the points (8, 12) and (x, 24) . Find the value of x.

Solution :

Slope of the line joining (-2, 6) and (4, 8) : 

m  =  (8 - 6)/(4 - (-2))

  =  2 / (4 + 2) 

  =  2/6

  =  1/3 -----(1)

Slope of the line joining (8, 12) and (x, 24) .

m  =  (24 - 12)/(x - 8)

  =  12/(x - 8) -----(2)

if lines are perpendicular to each other, the product of the slopes is equal to -1.

Then, 

(1/3) ⋅ 12/(x - 8) =  -1

4/(x - 8)  =  -1

4  =  -(x - 8)

4  =  -x + 8

x  =  8 - 4

x  =  4

Apart from the stuff given above, if you need any other stuff in math, please use our google custom search here.

Kindly mail your feedback to 

We always appreciate your feedback.

©All rights reserved. onlinemath4all.com

How do you find the missing value using the given slope?