Question

what is an equation of the line that passes through the points (-1, -7) and (-8, 0)?

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, \((x_1, y_1)=(-1, -7)\) and \((x_2, y_2)=(-8, 0)\). So, \( m=\frac{0 - (-7)}{-8 - (-1)}=\frac{7}{-7}=-1 \).

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 \((-1, -7)\) and \( m = - 1 \). Substitute these values into the formula: \( y - (-7)=-1(x - (-1)) \), which simplifies to \( y + 7=-1(x + 1) \).

Step3: Simplify to slope - intercept form

Expand the right - hand side: \( y+7=-x - 1 \). Then, subtract 7 from both sides to get \( y=-x - 8 \). We can also write it in standard form \( x + y=-8 \), but the slope - intercept form is a common form for the equation of a line.

Answer:

The equation of the line is \( y=-x - 8 \) (or \( x + y=-8 \))