Question

How do you find the missing value in the ordered pair \[(3, - 2),(x,6)\] and slope is “-4”?

Answer 1

Hint: The given question needs to be solved with the help of the line equation that can be formed by using the given two points and the slope which is given in the question, by using both the equation we can solve for the coordinate. This question needs to compare the value of slope which is found by the line equation and the slope given in the question.

Formulae Used:\[ y - {y_1} = \dfrac{{{y_2} - {y_1}}}{{{x_2} - {x_1}}}x - {x_1}\]

Complete step by step solution:
The given question need to be solved by first creating the line equation
that can be formed by using the coordinates given in the question:
The two coordinates are \[(3, - 2),(x,6)\]
Forming the line equation by the general equation of line for any two coordinate as:
 \[ \Rightarrow y - {y_1} = \dfrac{{{y_2} - {y_1}}}{{{x_2} - {x_1}}}x - {x_1}\]
Using this equation in our question we get:
\[ \Rightarrow y - ( - 2) = \dfrac{{6 - ( - 2)}}{{x - 3}}x - 3\]
\[ \Rightarrow y + 2 = \dfrac{8}{{x - 3}}x - 3\]
On solving we get the slope as \[\dfrac{8}{{x - 3}}\]
On comparing the slope with the given slope in the question which is “-4”
We get:
\[
   \Rightarrow \dfrac{8}{{x - 3}} = - 4 \\
   \Rightarrow 8 = - 4(x - 3) \\
   \Rightarrow 8 = - 4x + 12 \\
   \Rightarrow 4x = 12 - 8 \\
   \Rightarrow x = \dfrac{4}{4} = 1 \\
 \]

Hence the value of the coordinate is “1”.

Note: The given question can be solved by comparing the slope of the given question and by the slope of the linear equation of line what we obtained using the coordinates, we have to solve this by using this method only. Here we cannot solve this by using the graphical approach because we cannot plot the graph with assumed variable coordinates.