Question

check the slope box and click and drag one of the labeled coordinate points to (-3, -4). click and move the second point to a point that has an x - coordinate x = 1 such that the slope of the line passing through the two points is \\(\frac{1}{2}\\).
use the interactive figure to find your answer.
click here to launch the interactive figure.
...
the coordinates of the second point are \\(square\\).
(type an ordered pair.)

Explanation:

Step1: Recall slope formula

The slope formula between two points \((x_1, y_1)\) and \((x_2, y_2)\) is \(m = \frac{y_2 - y_1}{x_2 - x_1}\). We know \(x_1=-3\), \(y_1 = - 4\), \(x_2 = 1\), and \(m=\frac{1}{2}\).

Step2: Substitute values into formula

Substitute into \(m=\frac{y_2 - y_1}{x_2 - x_1}\): \(\frac{1}{2}=\frac{y_2 - (-4)}{1 - (-3)}\)
Simplify the denominator: \(1 - (-3)=4\), so \(\frac{1}{2}=\frac{y_2 + 4}{4}\)

Step3: Solve for \(y_2\)

Cross - multiply: \(y_2+4=\frac{1}{2}\times4\)
Calculate \(\frac{1}{2}\times4 = 2\), so \(y_2+4 = 2\)
Subtract 4 from both sides: \(y_2=2 - 4=-2\)

Answer:

\((1, - 2)\)