Question

Write the equation of the line that passes through the points (3,1)(3,1) and (-7,-1)(−7,−1). Put your answer in fully simplified point-slope form, unless it is a vertical or horizontal line.

Answer 1

`\textsf{Point-slope form}: \quad y-1=(1)/(5)(x-3)`

Explanation:

Define the given points:

• (x₁, y₁) = (3, 1)
• (x₂, y₂) = (-7, -1)

Substitute the defined points into the slope formula to find the slope of the line:

`\implies \textsf{Slope $(m)$}=(y_2-y_1)/(x_2-x_1)=(-1-1)/(-7-3)-(-2)/(-10)=(1)/(5)`

Substitute the found slope and one of the points into the point-slope formula:

`\implies y-y_1=m(x-x_1)`

`\implies y-1=(1)/(5)(x-3)`

Simplify to slope-intercept form, if necessary:

`\implies y-1=(1)/(5)x-(3)/(5)`

`\implies y=(1)/(5)x+(2)/(5)`