equation of a straight line in intercept form and sketch graphs

x
Given the gradient m and one other point P1(x1，y1) ：
y-y1=m(x-x1)
gradient form： y = mx + c m: the gradient of the line c: the y-axis intercept
提出问题：
Often we encounter a linear relation that is not expressed in the form y = mx + c. An alternative standard notation is ax + by = c This is sometimes referred to as the intercept form.
What have you learn from this class?
1.Find the equation of a straight line in intercept form 2.Sketch the graph of a straight line by finding the intercepts
Solution
Exerciss of each of the following linear relations: a. 2x − 3y = 12 b. x − 4y = 8 c .−3x + 4y = 24

A straight line has equation y = 3x − 4. The points with coordinates (0, a), (b, 0), (1, d ) and (e, 10) lie on the line. Find the values of a, b, d and e.
Example 16
Find the equation, in intercept form, of the line passing through the points A(2, 5) and B(6, 8).
85 3 m 62 4 Therefore, using the gradient and the point A(2, 5), we have the equation: 3 y 5 ( x 2) 4 4(y − 5) = 3(x − 2) 4y − 20 = 3x − 6 4y − 3x = 14 −3x + 4y = 14
Example
For the straight line with equation ax + by = c（ab≠0）.Find the x-axis intercept y and y-axis intercept. Solution: x-axis intercept (y = 0): c ax + b(0) = c, x = a y-axis intercept (x = 0): c a(0) + by = c, y =
REVIEW
Given any two points on the line, y the line： P1(x1，y1), P2(x2，y2),the gradient of

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y2 y1 gradient=m x2 x1

( x1 x2 )
0
P1(x1,y1)
●
P2(x2,y2)
b
y-axis ● Q intercept
P
0
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x
x-axis intercept
Note : plot the two axes intercepts is a convenient way to sketch graphs of straight lines
Example 15 Sketch the graph of 2x + 4y = 10. Solution x-axis intercept (y = 0): 2x + 4(0) = 10，x = 5 y-axis intercept (x = 0): 2(0) + 4y = 10，y = 2.5
Example 17
Sketch the graph of y = 2x − 6, by first finding the intercepts.
Solution When x = 0, y=−6. Hence the y-axis intercept is −6. When y = 0, 2x − 6 = 0 ∴ 2x = 6 and x = 3 The x-axis intercept is 3.