Question

Find the slope of the line passing through the pair of points. \((-4,-2)\) and \((-1,3)\)

Short answer

The slope of the line passing through the pair of points \((-4, -2)\) and \((-1, 3)\) is \(m = \frac{5}{3}\).

Step-by-step solution

Identify the given points as coordinate pairs

Let's identify the two points given in the problem: point A \((-4, -2)\) and point B \((-1, 3)\).

Apply the slope formula

Now we will apply the slope formula using the two given points, A and B. Remember, the slope formula is: \[m = \frac{y_2 - y_1}{x_2 - x_1}\].

Substitute the given values into the formula

Substitute the coordinates of the given points into the formula: \(m = \frac{3 - (-2)}{-1 - (-4)}\)

Simplify the numerator and denominator

Now let's simplify the numerator and denominator of the fraction: Numerator: \(3 - (-2) = 3 + 2 = 5\) Denominator: \(-1 - (-4) = -1 + 4 = 3\) So the simplified fraction is: \(m = \frac{5}{3}\)

Write the final answer

The slope of the line passing through the pair of points \((-4, -2)\) and \((-1, 3)\) is \(m = \frac{5}{3}\).