Transcription of The slope-intercept form - Mathematics resources
1 The slope -intercept formmc-bus- slope -2009-1 IntroductionOne form of the equation of a straight line is called theslope- interceptform because it containsinformation about these two equation of a straight lineAny equation of the formy=mx+cwheremandcare fixed numbers, ( constants), has a graph which is a straight example,y= 3x+ 5,y=23x+ 8andy= 3x 7all have graphs which are straight slope and intercept of a straight lineIn the equationy=mx+cthe value ofmis called theslope, (or gradient), of the line . It can bepositive, negative or zero. Lines with a positive gradient slope upwards, from left to right. Lines witha negative gradient slope downwards from left to right. Lines with a zero gradient are line has a positive gradientthis line has a negative gradientthe gradient of this line is zeroyyxxThe value ofcis called thevertical interceptof the line . It is the value ofywhenx= 0. Whendrawing a line ,cgives the position where the line cuts the vertical vertical intercept is negativeythe vertical intercept is mathcentre 2009 ExampleDetermine the gradient and vertical intercept of each )y= 12x 6, b)y= 5 2x, c)4x y+ 13 = 0, d)y= 8, e)y= ) Comparingy= 12x 6withy=mx+cwe see thatm= 12, so the gradient of the line is fact that this is positive means that the line slopes upwards as we move from left to right.
2 Thevertical intercept is 6. This line cuts the vertical axis below the horizontal ) Comparingy= 5 2xwithy=mx+cwe see thatm= 2, so the gradient is 2. The lineslopes downwards as we move from left to right. The vertical intercept is ) We write4x y+ 13 = 0in standard form asy= 4x+ 13and note thatm= 4,c= ) Comparingy= 8withy=mx+cwe see thatm= 0andc= 8. This line is ) Comparingy= 4xwithy=mx+cwe see thatm= 4andc= State the gradient and intercept of each of the following )y= 5x+ 6, b)y= 3x 11, c)y= 2x+ 7,d)y= 9, e)y= 7 xAnswers1. a) gradient 5, intercept 6 b) 3, 11, c) 2,7, d)0,9, e) 1, about the gradientThe gradient measures the steepness of the line . A large positive value ofmmeans the graphincreases steeply as you move from the left to the right. A small, but positive value ofmmeans thegraph increases, but not very steeply. Similarly, a large negative value ofmmeans that the graphdrops steeply as you move from left to right. A small negativevalue means the graph decreases,but not very fact we can say more.
3 The value ofmtells us the amount by whichyincreases (or decreases) ifxincreases by one example, for the liney= 5x+ 13, the value ofyincreases by 5 units every timexincreases by1 the liney= 3x+ 7the value ofydecreases by 3 units every timexincreases by 1 unit. Youshould sketch these graphs to convince yourself of this IfP= 4Q+ 9, by what amount willPincrease ifQincreases by 1 unit ?2. IfP= 11 3Q, by what amount willPdecrease ifQincreases by 1 unit ?3. IfP= 19, by what amount willPincrease ifQincreases by 1 unit ?Answers1. 4. 2. It will not. The value ofPis constant, that is fixed at 19. It does not depend mathcentre 2009
