Unit 3.2 Lines: Section A Notes. X is always before y in a set of points in an equation. (x,y) Always read plots from left to right. Vertical Lines: Vertical which is described in the equation X= A . Its described purely in a run value, and the point is on the Y axis only. In the (x,y) setting points would look like this (0, any number) means vertical line. Writing an equation with (Y intercept and slope only) y=mx+b is the “everybody else formula” in lines and graphing equations. “ B” in this formula is always the y intersect on the graph, and the starting point in the graph. If a line has a slope, or a rise over a run, it will tilt in any direction going up or down. For example if the y intersect is -1 (b value) and the slope is ½ the equation would be written as y = 1/2x -1 No Slope & Y intercept Horizontal lines are found in the “y” axis. The plots for a horizontal line, look like this (any #, 0) A Horizontal equation would be written like this: Y= 0x + (y axis point) because there is zero slope, m=0, or x0 simply find the intersect (b) and draw the line across If B equals 3, three would be plotted on the y axis ----------->3-------- Find the slope: or “m”: The (Y 2 –Y2) and (X2 ,X-1 fractions) formula is used When a pair of plots are given, (2,-10) and (12,15) M= 15 - (-10) = 25 = 5 12 – 2 10 2 The result is a positive slope and the line goes up. (negative of course is the reverse A horizontal m result would look like the 0/11. No slope Vertical lines look like this 3/0. Plots with a variable and an m value: (5,2) (x, 2) would still use the (Y 2 –Y2) and (X2 ,X-1 fractions) formula to find the variable. -2-2 = 2 simply then distribute to give a common denominator x-5 m= - 4 = 2(x-5) clear fractions and distribute x-5 -4x – 20 = 2x -10 -2x = -6 divide both sides by -2 to get x alone leaves x = 3 Graphing Lines with an equation already given: An equation like y = 2x +3 or y = mx+b 1st find the slope.. because 2 is times x, the m value in fraction form is 2/1. Giving a rise of two over a run of 1. B, the “y” value, +3 is the starting point in the equation on the “y” axis. Solving equations to find slope: getting y alone. Y=mx+b 4x+5y= 20 first begin get y alone by moving x 5y = -4x +20 Then divide each side by 5 to get y alone. 5y = -4x+20 leaves y = -4 x +4 slope is -4/5 and 5 5 5 the b value is 4. Equation of a line with one set of points given and the slope: (-1/3, 2) slope -3 still need to use the (X and Y) labels. And the y=mx+b formula 2=(-1/3 *-3) +b -3 and neg one third cancel to one. 2= 1+b subtract one to leave 1=b The rewrite with the y=mx+b answer y = -3x+1 Section D Notes Y= mx+b Find the Equation when there are two pairs of points given: (this equation is used twice) after “m” is found. Once to solve for “b” and once to write the final equation) First find the slope m=rise over run using the values given in the brackets using y2-y1 /x2-x1 formula. (2,4) (-3,-1) this is also the same order in the points (X 1, Y1) and (X2 ,Y2) to label the points -1-4 leaving 3 -3-2 3 which reduces to 1 this is the slope or “m” value Then find “b”, with either of the pairs given Then plug in the y=mx+b with either pair of points. Remember to place the “m” value in the equation and to solve for “b” the first time. I am going to use (-3,-1) (x,y)order stays the same. Equation is this: -1 = 1(1) +b -1 in the place of “y”, because it falls in the y column, -1 is multiplied by +1 because it is the “mx” part, Then simply +b. Leaving -1= 1+b subtract 1 from -1 leaving -2 and leaving b= -2 (think get b alone, lol) Rewrite the equation y=mx+b now that we have “b” y = 1x-2 or (y= slope times x +b)
Posted on: Fri, 23 Jan 2015 00:47:29 +0000
Trending Topics
Recently Viewed Topics
© 2015