Question

what is an equation of the line that passes through the points (1, -7) and (-1, 5)?
answer attempt 1 out of 100

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, \((x_1,y_1)=(1, - 7)\) and \((x_2,y_2)=(-1,5)\). So, \( m=\frac{5-(-7)}{-1 - 1}=\frac{5 + 7}{-2}=\frac{12}{-2}=-6 \).

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 \((1,-7)\) and \( m=-6 \). Substitute these values into the formula: \( y-(-7)=-6(x - 1) \), which simplifies to \( y + 7=-6x+6 \). Then, subtract 7 from both sides to get the slope - intercept form: \( y=-6x+6 - 7=-6x - 1 \). We can also write it in standard form \( 6x+y=-1 \).

Answer:

\( y=-6x - 1 \) (or \( 6x + y=-1 \))