5.5 Point-Slope Form of a Linear Equation

You can use the point-slope form when you are given the slope and a point on theline. In the point-slope form, (x 1 , y 1 ) is the given point and (x, y) is any otherpoint on the line. You can also use the point-slope form when you are given twopoints on the line. First find the slope. Then use either given point as (x 1 , y 1 ).EXAMPLE 2Using the Point-Slope FormSTUDENT HELPHOMEWORK HELPVisit our Web sitewww.mcdougallittell.comfor extra examples.INTERNETWrite an equation of the line shown at the right.SOLUTIONFirst find the slope. Use the points(x 1 , y 1 ) = (º3, 6) and (x 2 , y 2 ) = (1, º2).(3, 6)53ym ==y 2 º y 1 x2 º x 1º2 º 6 1 º(º3)53111 3 x(1, 2)= º 84STUDENT HELPStudy TipThe point-slope formy – y 1 = m(x – x 1 ) hastwo minus signs. Be sureto account for thesesigns when the point(x 1 , y 1 ) has negativecoordinates.= º2Then use the slope to write the point-slope form. Choose either point as (x 1 , y 1 ).y º y 1 = m(x º x 1 )Write point-slope form.y º 6 = º2[x º (º3)] Substitute for m, x 1 , and y 1 .y º 6 = º2(x + 3) Simplify.y º 6 = º2x º 6Use distributive property.y = º2xAdd 6 to each side.ACTIVITYDevelopingConceptsInvestigating the Point-Slope FormThe line shown at the right is labeledwith four points.1Each person in your group shoulduse a different pair of points towrite an equation of the line inpoint-slope form.y(5, 4)(2, 2)42(1, 0)5 3 13 5x2Compare the equations of thepeople in your group. Discusswhether the following statementseems to be always, sometimes, ornever true. Any two points on a linecan be used to find an equation of the line.24(4, 2)5.5 Point-Slope Form of a Linear Equation 301