Chapter 1 Section 1.1

Chapter 2 Section 2.3LinesPrepared by Doron ShaharWarm-up: Class Notes Page 25 Today we are starting to learn about lines. In honor of that, here are several one-liners:I wondered why the Frisbee was getting bigger, and then it hit me.

I had a dream I was eating a giant marshmallow, and when I woke up my pillow was missing!

Right now I'm having amnesia and deja vu at the same time! I think I've forgotten this before?

Hows that new line I introduced you to? Ohh, she goes on forever.Prepared by Doron ShaharFind points on a graph(2,3)(2,1)x coordinate firsty coordinate second(x , y)Prepared by Doron ShaharFinding intercepts on a graph(0,2)(4,0)x-intercepty-interceptwhere line touches y-axiswhere line touches x-axisPrepared by Doron ShaharFind slope from a graphRise

Run

Prepared by Doron ShaharThe slope of a line passing through two distinct points

(x1, y1) and (x2, y2) is given by the formula____________ Exception: The slope is undefined if x1=x2.

Slope formulaExtra 1: Find the slope of the line passing through the points (2, 3) and (4, 5).

(x1, y1) and (x2, y2)

Prepared by Doron ShaharSlope-intercept formThe slope-intercept form of the equation of a line with slope m and y-intercept (0, b) is given by the formula _____________

2.3.4 Find the slope-intercept form of the equation of the line with y-intercept (0, 8) and having slope m=2/5.

SolutionPrepared by Doron ShaharExtra 2: Slope-intercept formFind the slope-intercept form of the equation of the line displayed in the graph below.(0, 3)y-intercept(2, 4)

(x1, y1)

(x2, y2)

SolutionPrepared by Doron Shahar2.3.4 Sketch a graphy-intercept:Sketch a graph of the line y=2/5x 8 .Slope:(0, 8)

+( )y-intercept2

5Two points define a line.Prepared by Doron Shahar2.3.4 Identifying interceptsFind the y-intercept and the x-intercept of the line y=2/5x8.To find the x-intercept, set y=0 and solve for x.

Setting y equal to zeroSolutionTo find the y-intercept, set x=0 and solve for y.

Setting x equal to zeroSolution

y-intercept:

x-intercept:Prepared by Doron ShaharPoint-slope formThe point-slope form of the equation of a line passing through the point (x1, y1) and having slope m is given by the formula

______________________

Extra 3: Find the point-slope form of the equation of the line passing through the point ( 3,2) with slope m= 2.

Solution(x1, y1)

Prepared by Doron ShaharExtra 4: Point-Slope formFind the point-slope form of the equation of the line passing through the points (1, 3) and (1, 4).

(x1, y1) and (x2, y2)First find the slope.

Solution

Solution

Prepared by Doron Shahar2.3.2: Point-slope formFind the point-slope form of the equation of the line displayed in the graph below.(4, 5)(2, 3)

First find the slope.(x1, y1)(x2, y2)

SolutionPrepared by Doron Shahar

Extra 3: Sketch a graphPoint:Sketch a graph of the line y2= 2(x+3).Slope:(3, 2)

Point2

1Two points define a line.Prepared by Doron Shahar2.3.2 Identifying InterceptsFind the y-intercept and the x-intercept of the line y5= 4(x+4).To find the x-intercept, set y=0 and solve for x.

Setting y equal to zeroSolutionTo find the y-intercept, set x=0 and solve for y.

Setting x equal to zeroSolution

y-intercept:

x-intercept:Prepared by Doron ShaharPoint-slope to Slope-intercept form2.3.2 Write the line y5=4(x+4) in slope-intercept form.

Starting EquationDistribute right hand side

Slope-intercept formPrepared by Doron Shahar16Standard form of a lineThe standard from of the equation of a line is given by the formula

__________________ , where A and B are not both zero.

2.3.1 Write x/3 4y +1 =0 in standard form such that A, B, C are integers.

Subtract 1 from both sides

Multiply both sides by 3Prepared by Doron Shahar2.3.1 Identifying InterceptsFind the y-intercept and the x-intercept of the line x12y= 3.To find the x-intercept, set y=0 and solve for x.

Setting y equal to zeroSolutionTo find the y-intercept, set x=0 and solve for y.

Setting x equal to zeroSolution

y-intercept:

x-intercept:Prepared by Doron Shahar2.3.1 Sketch a graphx-intercept:Sketch a graph of the line x12y= 3.(3, 0)Two points define a line.y-interceptx-intercepty-intercept:(0, 1/4)Prepared by Doron ShaharStandard formEvery line can be written in standard form. This is not true of the other two forms. In particular, verticals lines can only be written in standard form, because their slope is undefined.

It is difficult to get the equation of a line directly into standard form given a graph or usual information. Instead, you will need to be able to get the equations of lines into and out of this form. Prepared by Doron ShaharPoint-slope to Standard formTo get the equation of a line from point-slope form into standard form, first convert it into slope-intercept form as we have already learned. Then proceed as on the next slide to convert the equation into standard form.Prepared by Doron ShaharSlope-intercept to Standard form2.3.4 Write the line y=2/5x8 in standard form such that A, B, and C are integers.

Starting EquationMultiply both sides by 5

Distribute the 5

Alternative Standard formPrepared by Doron Shahar22Standard to Slope-intercept to form2.3.1 Write the line x12y = 3 in slope-intercept form.

Starting EquationSubtract x from both sides

Divide by 12

Slope-intercept formPrepared by Doron Shahar23Standard to Slope-intercept formOne reason for converting the equation of a line from Standard form to slope-intercept form is to find the slope of the line. It also helps if you are trying to graph the line.2.3.1 Find the slope of the x12y = 3.

Slope-intercept formSlope:

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Turtle

Sign language for turtle

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Horizontal lines2.3.5 Write the equation of the horizontal line passing through the point (9/2, 15/2).

A horizontal line passing through the point (a, b) is given by the equation ________.The slope of a horizontal line is _________.

SolutionPrepared by Doron ShaharExtra 5: Horizontal linesFind the equation of the horizontal line displayed below.

Solution(2, 3)(a, b)Prepared by Doron Shahar2.3.5 Sketch a graphSketch a graph of the line y=15/2.Slope:

(9/2, 15/2)Prepared by Doron Shahar2.3.5 Identifying interceptsFind the y-intercept and the x-intercept of the line y=15/2.To find the x-intercept, set y=0 and solve for x.

Setting y equal to zeroTo find the y-intercept, set x=0 and solve for y.

Setting x equal to zeroSolution

y-intercept:There is no x-intercept!PROBLEMA!

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Vertical lines2.3.3 Write the equation of the vertical line with x-intercept (1/3, 0).

SolutionA vertical line passing through the point (a, b) is given by the equation ________.The slope of a vertical line is _____________.

Prepared by Doron ShaharExtra 6: Vertical linesFind the equation of the vertical line displayed below.

Solution(2, 3)(a, b)Prepared by Doron Shahar2.3.3 Sketch a graphSketch a graph of the line x=1/3.Slope:

(1/3, 0)Prepared by Doron Shahar2.3.3 Identifying interceptsFind the y-intercept and the x-intercept of the line x=1/3.To find the x-intercept, set y=0 and solve for x.

Setting y equal to zeroTo find the y-intercept, set x=0 and solve for y.

Setting x equal to zeroSolution

x-intercept:There is no y-intercept!PROBLEMA!

Prepared by Doron ShaharHorizontal lines vs. Vertical linesHorizontal LinesVerticals linesEquationSlopex-intercepty-intercept

Exception: y=0

Exception: y=0

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