Question

a line passes through the points (4, -8) and (6, -9). write its equation in slope-intercept form.
write your answer using integers, proper fractions, and improper fractions in simplest form.

Explanation:

Step1: Find the slope (m)

The slope formula between two points \((x_1, y_1)\) and \((x_2, y_2)\) is \(m = \frac{y_2 - y_1}{x_2 - x_1}\). Here, \(x_1 = 4\), \(y_1 = -8\), \(x_2 = 6\), \(y_2 = -9\). So, \(m=\frac{-9 - (-8)}{6 - 4}=\frac{-9 + 8}{2}=\frac{-1}{2}\).

Step2: Use point - slope form to find the equation

The point - slope form is \(y - y_1 = m(x - x_1)\). Let's use the point \((4,-8)\). Substitute \(m = -\frac{1}{2}\), \(x_1 = 4\), \(y_1 = -8\) into the formula: \(y - (-8)=-\frac{1}{2}(x - 4)\), which simplifies to \(y + 8=-\frac{1}{2}x+2\).

Step3: Convert to slope - intercept form (\(y = mx + b\))

Subtract 8 from both sides: \(y=-\frac{1}{2}x + 2-8\), so \(y = -\frac{1}{2}x-6\).

Answer:

\(y = -\frac{1}{2}x - 6\)