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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 ?

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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Mathematics
6 months
2021-07-31T13:12:17+00:00
2021-07-31T13:12:17+00:00 2 Answers
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## Answers ( )

Answer: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.

Answer:Step-by-step explanation:We have the two points (3

a, 4) and (a, -3).And we want to find the value of

asuch 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 (3

a,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: