3-433.4The Point-Slope Form2113.4The Point-Slope FormIn Section 3.3 we wrote the equation of a line given its slope and y-intercept. In thissection, you will learn to write the equation of a line given the slope and anypointon the line.In This SectionU1VPoint-Slope FormU2VParallel LinesU3VPerpendicular LinesU4VApplicationsU1VPoint-Slope FormConsider a line through the point (4, 1) with slope 23as shown in Fig. 3.29. Because theslope can be found by using any two points on the line, we use (4, 1) and an arbitrarypoint (x,y) in the formula for slope:yx22yx11mSlope formulayx1423Let m23, (x1, y1)(4, 1), and (x2, y2)(x, y).y123(x4)Multiply each side by x4.UHelpful Hint VIf a point (x,y) is on a line with slopemthrough (x1,y1), thenm.Multiplying each side of this equationby xx1gives us the point-slopeform.yy1xx1Note how the coordinates of the point (4, 1) and the slope 23appear in the preceding equation. We can use the same procedure to get the equation of any line given onepoint on the line and the slope. The resulting equation is called the point-slope formof the equation of the line.Figure 3.29yx43313211(4, 1)(x, y)231Miscellaneous.18.Find the slope of the line through (3, 4) and (1, 1).19.Draw the graph of a line through the origin with slope 34.20.Is the line through (2, 1) and (3, 5) parallel or perpendic-ular to the line through (4, 0) and (0, 5)?