Question

through: (1, 2) and (0, -5)

Explanation:

Step1: Find 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, \((x_1,y_1)=(1,2)\) and \((x_2,y_2)=(0, - 5)\). So \( m=\frac{-5 - 2}{0 - 1}=\frac{-7}{-1}=7 \).

Step2: Use slope - intercept form

The slope - intercept form of a line is \( y = mx + b \), where \( m \) is the slope and \( b \) is the y - intercept. We know that the line passes through \((0,-5)\), which is the y - intercept (\(x = 0\) gives \(y=b\)). So \( b=-5 \).

Step3: Write the equation

Substitute \( m = 7 \) and \( b=-5 \) into \( y=mx + b \). We get \( y = 7x-5 \).

Answer:

The equation of the line is \( y = 7x-5 \)