2.3 – Linear Functions and Slope Lesson
I. Slope: Watch the video linked by the following QR code and follow along.
Slope m=riserun=change in ychange in x=y2-y1x2-x1
Find the slope of the line containing
the points (-4,3) and 2,-6.
Find the slope of the line y=4.
Find the slope of the line x=-3.
After you are finished with the video:
Practice: Find the slope of the line containing the following pairs of points.
a.) (2,-3) and (-1,5) b.) (0,3) and (3,0)
II. Finding an Equation of a Line: Scan the QR code and watch/follow along.
Point-Slope Form: y-y1=m(x-x1)
(1) Slope =12 through (4,4).
(go to the next page)
Point-Slope Form: y-y1=m(x-x1)
(2) Through (-2,4) and (4,-5).
After watching the video:
Practice: Find an equation of the line passing through the points (3,-2) and (5,1). Write the equation in slope-intercept form y=mx+b, and sketch the graph. (Hint: You are doing the same thing as the two previous examples.)
III. Standard Form for the Equation of a Line: Scan the next QR code, watch and follow along with the video.
(go to the next page)
Standard Form: Ax+By=C
2x-3y=6 -3x+y=9
IV. Go From Standard Form to Slope-Intercept Form: Watch the next video.
Rewrite the given equation in slope-intercept form.
1. x+y=25 4. 4x-y=12
11. 2x+40y=80 18. 5x-7y=-28
(go to the next page)
V. Parallel and Perpendicular Lines: Scan the next QR code.
y=3x+2
y=3x-3
y=-23x+4
y=-23x-1
y=3x+2
y=-13x-3
y=-23x+4
y=32x-1
Example 1: Determine the equation of the line that is parallel to 3x+2y=12 and passes through (2,-5). Write the line in slope-intercept form. You may check by graphing. (Hint: Use the QR code to walk through the example.)
Example 2: Determine the equation of the line that is perpendicular to y=2x+1 and passes through (-4,5). You may check by graphing. (Hint: Use the QR code for a walkthrough of this problem.)
VI. Problems:
1. Find an equation of the line passing through the point (6,-2) with slope -23.
2. Find an equation of the line passing through the points (-3,-1) and (2,4).
3. Find an equation of the line with x-intercept = 4 and y-intercept = -2.
4. Find an equation of the line passing through -8,-10 and parallel to the line whose equation is y=-4x+3.
5. Find an equation of the line passing through -4,2 and perpendicular to the line whose equation is y=13x+7.