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Standard FormParallel LinesPerpendicular LinesSlope on graphSlope using 2 points*Always begin on the left side at a point.2Count up (+) or down (-) and place # in numerator.<Then count right (+) or left (-) and place # in denominator.positive slopenegative sloperise run1st point is (x1,y1) 2nd point is (x2,y2) %y2 - y1 x2 - x1!$/subtracting a negative is like adding a postiveslope = 0 y=#(If answer has zero on top then slope = 00If answer has zero on the bottom then undefined.slope is undefined x=#Also known as b!Where the line crosses the y-axis'Can be found by using a point and slope%b=0 when line goes through the originy=mx + bAlso known as mWhere x=0 Point is (0,b)DPlot this point (0,b) FIRST when graphing a slope intercept equation-Ex: m=2 (4,-1) -1=2*4 + b -7=bIn standard form, (y-int) b=C/BAx + By = Cm= -A/BJTo graph the equation plot the x-int and y-int points and draw the line. 6Graph by plotting the y-intercept first on the y-axis.@Next make slope into a fraction and follow slope counting rules.@Example: y=-2/3x - 3 plot (0,-3) then count down 2 and right 3/To find x-int. replace y with 0 and solve for x!Where the line crosses the x-axis1Where y=0 Point (x-int, 0)TEx: 5x-2y=10 5x-2*0=10 5x=10 x=2 point (2,0)vEx.: y= -3x +9 0= -3x +9 -9= -3x x=3 point (3,0)/Write equation by finding slope and y-interceptPEx: (4,2) (0,-4) m=(-4 - 2)/(0-4)= -6/-4=3/2 y-int (0,-4) y=3/2x - 45Draw a line thru the 2 plotted points and check slopeREx: y=3x-4 (5,2) replace x and y to find new b. 2=3*5 + b b=-13 y=3x -13!Rewrite new equation at the end!!.Slope-intercept form Same y=mx but different b+Standard form same Ax + By but different C9Ex: 2x-5y = 8 (1,-1) 2*1 - 5*-1 = C C=7 2x-5y = 72Slope-intercept form slope is opposite reciprocal.0Find new m then find new b by using given point.9Standard form flips the coefficients and change the sign.;Use the new equation with the given point to find the new CZEx1: 2x - 5y = 10 new 5x + 2y = C Ex2: x + 4y = 6 new 4x - y = CDEx1:original m= 2 new m= -1/2 Ex2:orig. m= -2/5 new m=5/2REx1: m=2 (4,3) 3= -1/2*4 +b 3= -2 + b 5=b y= -1/2x + 5jEx1: 5x+2y=C (1,-1) 5*1 + 2*-1= C 3=C 5x + 2y = 3!x-int = C/A y-int = C/B-Check to ensure the slope of line is correct.CWrite an equation using slope and one point with the slope formula.8Remember if slope is opposite of the sign in this case!!>Use slope rules to place in Ax+/-By=C then use (x,y) to find CR_703@M-
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