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

Question

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

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6 months 2021-07-31T13:12:17+00:00 2 Answers 84 views 0

Step-by-step 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

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

Step-by-step 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:

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:

Simplify:

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

Solve for a. Rewrite:

Cross-multiply:

Therefore: