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2.4 Equation of a straight line in intercept form and sketching graphs

1. Intercept form

? ax + by = c intercept form ? Note: It is necessary to transpose the equation into gradient form if you wish to ?nd the gradient. ? Eg1. Give the gradient for the line: 2x+4y=10 ? Solution: 2x+4y=10 ? 4y=10-2x ? Intercept form

5 x y? ? 2 2

10 ? 2 x y? 4

1 ? The gradient of the line is ? 2

Eg2. Find the equation, in intercept form, of the line passing through the pointsA(2,5)and B(6,8)

8?5 3 Solution : m ? ? 6?2 4

? y-y1=m(x-x1)

3 y ? 5 ? ( x ? 2) 4

? 4(y-5)=3(x-2)

? -20=3x-6-4y ? 3x-4y=-14

? 4y-20=3x-6 ? -14=3x-4y

Eg3. To sketch, find x and y intercept of 2x-y=4. ? y intercept x=0 -y=4 ? x intercept y=0 2x=4 y ? y=-4 ? x=2

o

2

-4

x

Eg4. Sketch the graph of y=2x-6, by first finding the intercept. ? y intercept x=0 ? Solution: y=2x-6 ? y=-6 ? x intercept y=0 0=2x-6 y ? x=3

o

-6

3

x

Homework ? ? ? ? ? ? ? P42 Exercise2D 1.a、c 2、 3、5、6、7. Key Words encounter expressed alternative standard notation transpose convenient axes linear

? ? ? ? ?

encounter 遇到 alternative 有选择的 notation 符号 convenient 方便的 linear 线性的

express 表示 standard 标准的 transpose 变形 axes坐标轴