2.3 Linear Functions and Slope Lesson

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

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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.