Notes for 2.4 Equations of Lines; Curve Fitting
(pp. 227 – 235)
Topics: Point Slope; Slope Intercept; Vertical; Horizontal;
Parallel and Perpendicular Lines; Applications
I. Writing the Equation of a Line Using Point-Slope Form (pp. 227 – 228)
* The point-slope form of the equation of a line comes from the original slope formula
, but with only one point known.
The line with the slope m passing through ( x
) has the equation, y – y
= m(x – x
) , which is
called the point-slope form of the equation of the line.
Ex. Find the equation of a line through (5, -2) with a slope of –4.
Ex. Find the equation of a line through (-1, 7) and (2, 1).
First you need to find ____________________.
* Graph these lines using your favorite (convenient) point and the slope (rise / run).
* To write the equation using point-slope, you must have the slope (find it if you need to) and any
point on the line.
* Make sure that you put arrows at the end of the graphed line and that you label the line with its
equation. Also, label the scale used on the axes.
II. Writing the Equation of a Line Using Slope-Intercept Form (pp. 228 – 229)
The line with slope m and y-intercept b has an equation, y = mx + b, which is called the slope-
intercept form of the equation of the line.
Ex. Find the slope and the y-intercept of 2 x – y = 1.
* Isolate a positive y .