Week 3: Student Response to Discussion

Stephen Houck

TuesdayJun 20 at 6:01am

Manage Discussion Entry

For one line to be parallel to another means that they have the same slope and, when extended to infinity, will never cross. Here, I will find the equation of a line parallel to the given line y=1/2x+3 and passing through a given point, identified by the ordered pair (4,-1). The result will be in slope-intercept form which identifies the y-intercept of the graphed line when x=0. The y-intercept is the distance on the y-axis from the origin (0,0).

y-y1=m(x-x1) Point-slope form

y-(-1)=1/2(x-4) Substitute the ordered pair for x1,y1, and ½ for m (the slope of the original line)

y+1=1/2x-2 Simplify by subtracting 1 from both sides of the equation

y=1/2x-3 Slope-intercept form

Since -1=1/2(4)-3 is correct, the line y=1/2x-3 goes through the point (4,-1). Since both lines have a slope of ½, they are clearly parallel.

For one line to be perpendicular to another, it means that the slope is the negative reciprocal of the slope of the given line. The result is that the lines will meet at right angles. To find the equation of a line perpendicular to y=1/2x+3 and passing through the point (4,-1) we begin by taking the negative reciprocal of the slope ½, which is -2.

y-y1=m(x-x1) Point-slope form

y-(-1)=-2(x-4) Substitute

y+1=-2x+8 Distribute

y=-2x+7 Subtract 1 from both sides = slope-intercept form

Since -1=-2(4)+7 is correct, the line passes through (4,-1) and the slope (-2) is then negative reciprocal of ½ so the lines are perpendicular.