Point Slope Form
Point-Slope form of a linear equation is \( y- y_1 = m( x-x_1) \) where \(m \) is the slope, \( (x_1, y_1 ) \) is a fixed point on the line, and \(x \) and \(y \) are variables.
When we graph a line from this equation, we will do it similarly to graphing from slope-intercept form. We will plot the point from the equation and use the slope, rise over run, to get to the next point. We will do this a third time and then draw the line.
Example 1: Graph the following linear equation in point-slope form: \( y-4 = \frac{1}{2}(x+3) \).
The point is: \( (-3, 4) \) and the slope is \( \large\frac{1}{2} \).
Plot the point \( (-3, 4) \). From the point, using the slope, go up \( 1 \) (from the point) and to the right \( 2\), this is the next point. Use the slope again to get to the third point. Draw a line through the three points to graph the line.
Plot the point \( (-3, 4) \). From the point, using the slope, go up \( 1 \) (from the point) and to the right \( 2\), this is the next point. Use the slope again to get to the third point. Draw a line through the three points to graph the line.
Quick Check
Given the linear equation in point-slope form, graph it: \( y−4=−\frac{1}{3}(x+1) \).
Quick Check Solutions
Given the linear equation in point-slope form, graph it: \( y−4=−\frac{1}{3}(x+1) \).
Quick Check Solutions