Question

what is an equation of the line that passes through the points (5, 5) and (-5, -7)?

Explanation:

Step1: Calculate the slope

The slope \( m \) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by \( m=\frac{y_2 - y_1}{x_2 - x_1} \). Here, \((x_1, y_1)=(5, 5)\) and \((x_2, y_2)=(-5, -7)\). So, \( m=\frac{-7 - 5}{-5 - 5}=\frac{-12}{-10}=\frac{6}{5} \).

Step2: Use point - slope form

The point - slope form of a line is \( y - y_1=m(x - x_1) \). Using the point \((5, 5)\) and \( m = \frac{6}{5} \), we have \( y - 5=\frac{6}{5}(x - 5) \).

Step3: Simplify to slope - intercept form

Expand the right - hand side: \( y - 5=\frac{6}{5}x-6 \). Then, add 5 to both sides: \( y=\frac{6}{5}x - 6 + 5=\frac{6}{5}x-1 \). We can also write it in standard form \( 6x - 5y=5 \) (by multiplying through by 5: \( 5y = 6x-5\Rightarrow6x - 5y = 5 \)).

Answer:

\( y=\frac{6}{5}x - 1 \) (or \( 6x-5y = 5 \))