Question

write the equation of the line that passes through the points (-7, 0) and (-3, -4). put your answer in fully simplified point - slope form, unless it is a vertical or horizontal line. answer attempt 1 out of 2

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, \( x_1=-7,y_1 = 0,x_2=-3,y_2=-4 \). So \( m=\frac{-4 - 0}{-3-(-7)}=\frac{-4}{4}=- 1 \).

Step2: Use point - slope form

The point - slope form of a line is \( y - y_1=m(x - x_1) \). We can use the point \((-7,0)\) (we could also use \((-3,-4)\)). Substitute \( m=-1,x_1=-7,y_1 = 0 \) into the formula: \( y - 0=-1(x - (-7)) \), which simplifies to \( y=-1(x + 7) \) or \( y-0=-1(x + 7) \) (in point - slope form with the point \((-7,0)\)) or if we use the point \((-3,-4)\), \( y-(-4)=-1(x - (-3)) \) which is \( y + 4=-1(x + 3) \).

Answer:

\( y - 0=-1(x + 7) \) (or \( y+4=-1(x + 3) \))