In grade 8, students used similar triangles to explain why the slope is the same between any two distinct points on a non-vertical line in the coordinate plane, and they derived the equation for a line intercepting the vertical axis at . In this lesson, students develop the point-slope form of a linear equation: . Students will be writing equations of lines in the next several lessons, and intercepts will not always be readily available. Point-slope form will require the least algebraic manipulation and allow students to focus on geometric properties.

Slope calculations are an important part of this lesson, so students begin with a Warm-up that helps them recall this concept. Then they use the definition of slope to build the point-slope equation. Finally, they practice writing and interpreting equations of lines in point-slope form. Students have the opportunity to construct a viable argument (MP3) when they explain their methods of calculating slope.