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

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:

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.

3: 2

step-by-step explanation:

shorter piece is 2: 3, so just reverse it, and you get 3: 2

describing distributions is one of the key skills you’ll need to earn a high score on the ap statistics exam. if you need proof of this, just flip through some past exam questions, which can be found at the collegeboard website. you’ll notice that the first free response question is almost always a question requiring you to look at a graph and describe it.

step-by-step explanation: just trying to get points sorry : (