Question

a line passes through the points (-2, -10) and (3, 5). write its equation in slope-intercept form.
write your answer using integers, proper fractions, and improper fractions in simplest form.

Explanation:

Step1: Calculate 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, \(x_1=-2\), \(y_1 = - 10\), \(x_2=3\), \(y_2 = 5\). So, \(m=\frac{5-(-10)}{3-(-2)}=\frac{5 + 10}{3 + 2}=\frac{15}{5}=3\).

Step2: Use point - slope form to find the equation

The point - slope form is \(y - y_1=m(x - x_1)\). We can use the point \((3,5)\) (we could also use \((-2,-10)\)). Substitute \(m = 3\), \(x_1=3\), \(y_1 = 5\) into the formula: \(y-5=3(x - 3)\).

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

Expand the right - hand side: \(y-5=3x-9\). Then, add 5 to both sides: \(y=3x-9 + 5\), so \(y=3x-4\).

Answer:

\(y = 3x-4\)