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Find the value of a if the line joining the points (3a,4) and (a, -3) has a gradient of 1 ?

User Ymerej
by
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2 Answers

4 votes

Answer:


(7)/(2)

Explanation:

Objective: Linear Equations and Advanced Thinking.

If a line connects two points (3a,4) and (a,-3) has a gradient of 1. This means that the slope formula has to be equal to 1

If we use the points to find the slope: we get


(4 + 3)/(3a - a)

Notice how the numerator is 7, this means the denominator has to be 7. This means the denomiator must be 7.


3a - a = 7


2a = 7


a = (7)/(2)

User Kanngard
by
8.2k points
2 votes

Answer:


\displaystyle a=(7)/(2)\text{ or } 3.5

Explanation:

We have the two points (3a, 4) and (a, -3).

And we want to find the value of a such that the gradient of the line joining the two points is 1.

Recall that the gradient or slope of a line is given by the formula:


\displaystyle m=(y_2-y_1)/(x_2-x_1)

Where (x₁, y₁) is one point and (x₂, y₂) is the other.

Let (3a, 4) be (x₁, y₁) and (a, -3) be (x₂, y₂). Substitute:


\displaystyle m=(-3-4)/(a-3a)

Simplify:


\displaystyle m=(-7)/(-2a)=(7)/(2a)

We want to gradient to be one. Therefore, m = 1:


\displaystyle 1=(7)/(2a)

Solve for a. Rewrite:


\displaystyle (1)/(1)=(7)/(2a)

Cross-multiply:


2a=7

Therefore:


\displaystyle a=(7)/(2)\text{ or } 3.5

User Ayush Bherwani
by
7.9k points

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