Question

what is an equation of the line that passes through the points (5, -6) and (-5, -4)?

Explanation:

Step1: Find the slope (m)

The slope formula is \( m = \frac{y_2 - y_1}{x_2 - x_1} \). Let \((x_1, y_1) = (5, -6)\) and \((x_2, y_2) = (-5, -4)\). Then \( m = \frac{-4 - (-6)}{-5 - 5} = \frac{-4 + 6}{-10} = \frac{2}{-10} = -\frac{1}{5} \).

Step2: Use point - slope form

The point - slope form of a line is \( y - y_1 = m(x - x_1) \). Let's use the point \((5, -6)\) and \( m = -\frac{1}{5} \). So \( y - (-6)=-\frac{1}{5}(x - 5) \), which simplifies to \( y + 6 = -\frac{1}{5}x + 1 \). Then subtract 6 from both sides: \( y=-\frac{1}{5}x + 1 - 6 \), so \( y = -\frac{1}{5}x - 5 \). We can also write it in standard form \( x + 5y=-25 \), but the slope - intercept form is also a valid equation of the line.

Answer:

The equation of the line is \( y = -\frac{1}{5}x - 5 \) (or \( x + 5y=-25 \))