Question

write an equation of the line that passes through the pair of points. (-4, -2), (4, 0)

Explanation:

Step1: Find the slope (m)

The formula for slope between two points \((x_1, y_1)\) and \((x_2, y_2)\) is \(m=\frac{y_2 - y_1}{x_2 - x_1}\).
For points \((-4, -2)\) and \((4, 0)\), \(x_1=-4\), \(y_1 = - 2\), \(x_2 = 4\), \(y_2=0\).
So \(m=\frac{0 - (-2)}{4 - (-4)}=\frac{0 + 2}{4 + 4}=\frac{2}{8}=\frac{1}{4}\).

Step2: Use point - slope form \(y - y_1=m(x - x_1)\)

We can use the point \((4,0)\) (we could also use \((-4,-2)\)).
Substitute \(m = \frac{1}{4}\), \(x_1 = 4\), \(y_1=0\) into the point - slope form:
\(y-0=\frac{1}{4}(x - 4)\)
Simplify the equation:
\(y=\frac{1}{4}x-1\) (We can also write it in standard form \(x-4y = 4\) or other equivalent forms, but slope - intercept form is common)

Answer:

\(y=\frac{1}{4}x - 1\) (or equivalent forms like \(x-4y=4\) or \(y - 0=\frac{1}{4}(x - 4)\))