Question

write the equation in point - slope form y - y1 = m(x - x1) for the line that contains the points (3, -5) and (5, -1)
y + 3 = 2(x - 5)
y - 3 = 2(x + 5)
y + 5 = 2(x - 3)
y - 5 = 2(x + 3)

Explanation:

Step1: Calculate the slope \( m \)

The formula for slope between two points \((x_1, y_1)\) and \((x_2, y_2)\) is \( m=\frac{y_2 - y_1}{x_2 - x_1} \). Given points \((3, - 5)\) and \((5, - 1)\), we have \( x_1 = 3,y_1=-5,x_2 = 5,y_2=-1 \). So \( m=\frac{-1-(-5)}{5 - 3}=\frac{-1 + 5}{2}=\frac{4}{2}=2 \).

Step2: Use point - slope form

Point - slope form is \( y - y_1=m(x - x_1) \). We can use the point \((3,-5)\) (we could also use \((5,-1)\)). Substitute \( x_1 = 3,y_1=-5,m = 2 \) into the formula. We get \( y-(-5)=2(x - 3) \), which simplifies to \( y + 5=2(x - 3) \).

Answer:

\( y + 5 = 2(x - 3) \) (the third option among the given choices, which is \( y + 5 = 2(x - 3) \))