Answer:
Step-by-step explanation:
We have the two points (3<em>a</em>, 4) and (<em>a</em>, -3).
And we want to find the value of <em>a</em> 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 (<em>x₁, y₁</em>) is one point and (<em>x₂, y₂</em>) is the other.
Let (3<em>a, </em>4) be (<em>x₁, y₁</em>) and (<em>a</em>, -3) be (<em>x₂, y₂</em>). Substitute:
Simplify:
We want to gradient to be one. Therefore, <em>m</em> = 1:
Solve for <em>a</em>. Rewrite:
Cross-multiply:
Therefore: