The slope of the line joining points \(A(3,-2)\) and \(B(x,4)\) is 2. What is the value of \(x\)?
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 6
The slope of a line measures how steeply it rises: the change in \(y\) divided by the change in \(x\) between any two of its points, \(m=\frac{y_2-y_1}{x_2-x_1}\). Here the slope is known and one coordinate is missing, so the formula gives one equation in \(x\).
Slope through A and B, equal to 2: \(\displaystyle \frac{4-(-2)}{x-3}=2\)
The rise is 6, so the run must be 3: \(6=2(x-3)\), \(x-3=3\)
The value of \(x\) is 6