Graphing - Slope-Intercept Form

1 - Slope-Intercept FormObjective: Give the equation of a line with a known slope and Graphing a line we found one method we could use is to makea table ofvalues. However, if we can identify some properties of the line, we may be able tomake a graph much quicker and easier. One such method is finding the slope andthe y-intercept of the equation. The slope can be represented bymand the y-intercept, where it crosses the axis andx= 0, can be represented by(0, b)wherebis the value where the graph crosses the vertical y-axis. Anyother point on theline can be represented by(x, y). Using this information we will look at the slopeformula and solve the formula ,(0, b),(x, y)Using the slope formula gives:y bx 0=mSimplifyy bx=mMultiply both sides byxy b=mxAddbto both sides+b+by=mx+bOur SolutionThis equation,y=mx+bcan be thought of as the equation of any line that as aslope ofmand a y-intercept ofb.

2 This formula is known as the Intercept Equation:y=m x+bIf we know the slope and the y-intercept we can easily find the equation that rep-resents the , y intercept= 3 Use the slope intercept equationy=mx+b mis the slope , bis they intercept1y=34x 3 Our SolutionWe can also find the equation by looking at a graph and finding the slope and the point where the graphcrosses the y-axis (0,3). This meansthe y-intercept is one other point and draw aslope triangle to find the slope . Theslope is 23y=mx+bSlope-intercept equationy= 23x+ 3 Our SolutionWe can also move the opposite direction, using the equation identify the slopeand y-intercept and graph the equation from this information. However, it will beimportant for the equation to first be in slope intercept form . If it is not, we willhave to solve it foryso we can identify the slope and the in slope intercept form : 2x 4y= 6 Solve fory 2x 2xSubtract2xfrom both sides 4y= 2x+ 6 Putxterm first 4 4 4 Divide each term by 4y=12x 32 Our SolutionOnce we have an equation in Slope-Intercept form we can graphit by first plottingthe y-intercept, then using the slope , find a second point andconnecting the 4 Recall the slope intercept formulay=mx+bIdenfity the slope , m,and they intercept, b2m=12, b= 4 Make the graphStarting with a point at the y-inter-cept of 4,Then use the sloperiserun, so we will rise1 unit and run 2 units to find the we have both points, connect thedots to get our View Note:Before our current system of Graphing , French Mathemati-cian Nicole Oresme, in 1323 sugggested Graphing lines that would look more like abar graph with a constant slope !

3 Example + 4y=12 Not in slope intercept form 3x 3xSubtract3xfrom both sides4y= 3x+12 Put thexterm first444 Divide each term by4y= 34x+ 3 Recall slope intercept equationy=mx+bIdenfitymandbm= 34, b= 3 Make the graphStarting with a point at the y-inter-cept of3,Then use the sloperiserun, but its nega-tive so it will go downhill, so we willdrop 3 units and run 4 units to findthe next we have both points, connect thedots to get our want to be very careful not to confuse using slope to find thenext point with3use a coordinate such as(4, 2)to find an individule point. Coordinates such as(4, 2)start from the origin and move horizontally first, and vertically starts from a point on the line that could be anywhere onthe graph. Thenumerator is the vertical change and the denominator is the horizontal with zero slope or no slope can make a problem seem very different. Zeroslope, or horiztonal line, will simply have a slope of zero which when multipliedbyxgives zero.

4 So the equation simply becomesy=boryis equal to the y-coor-dinate of the graph. If we have no slope , or a vertical line, the equation can t bewritten in slope intercept at all because the slope is undefined. There is noyinthese equations. We will simply makexequal to the x-coordinate of the the equation of the line in we have a vertical line and noslope there is no Slope-Intercept equa-tion we can use. Rather we makexequal to the x-coordinate of 4x= 4 Our SolutionBeginning and Intermediate Algebra by Tyler Wallace is licensed under a Creative CommonsAttribution Unported License. ( ) Practice - slope -InterceptWrite the Slope-Intercept form of the equation of each line given theslope and the ) slope = 2, y-intercept = 53) slope = 1, y-intercept = 45) slope = 34, y-intercept = 17) slope =13, y-intercept = 12) slope = 6, y-intercept = 44) slope = 1, y-intercept = 26) slope = 14, y-intercept = 38) slope =25, y-intercept = 5 Write the Slope-Intercept form of the equation of each )11)13)10)12)14)515)x+10y= 3717)2x+y= 119)7x 3y=2421)x= 823)y 4 = (x+ 5)25)y 4 = 4(x 1)27)y+ 5 = 4(x 2)29)y+ 1 = 12(x 4)16)x 10y= 318)6x 11y= 7020)4x+ 7y=2822)x 7y= 4224)y 5 =52(x 2)26)y 3 = 23(x+ 3)28)0 =x 430)y+ 2 =65(x+ 5)Sketch the graph of each )y=13x+ 433)y=65x 535)y=32x37)x y+ 3 = 039) y 4 + 3x= 041) 3y= 5x+ 932)y= 15x 434)y= 32x 136)y= 34x+ 138)4x+ 5 = 5y40) 8 = 6x 2y42)

5 3y= 3 32xBeginning and Intermediate Algebra by Tyler Wallace is licensed under a Creative CommonsAttribution Unported License. ( ) - slope -Intercept1)y= 2x+ 52)y= 6x+ 43)y=x 44)y= x 25)y= 34x 16)y= 14x+ 37)y=13x+ 18)y=25x+ 59)y= x+ 510)y= 72x 511)y=x 112)y= 53x 313)y= 4x14)y= 34x+ 215)y= 110x 371016)y=110x 31017)y= 2x 118)y=611x+701119)y=73x 820)y= 47x+ 421)x= 822)y=17x+ 623)y= x 124)y=52x25)y= 4x26)y= 23x+ 127)y= 4x+ 328)x= 429)y= 12x+ 130)y=65x+ 431)32)33)34)35)36)37)38)39)40)41)42)7 Beginning and Intermediate Algebra by Tyler Wallace is licensed under a Creative CommonsAttribution Unported License. ( )8