| Example Find the equation of a straight line through (4, -1) which has a slope = 2/3 Solution : Using the slope point form i.e. y - y1 = m(x - x1) We get, y - (-1) = y + 1 = 3 (y + 1) = 2 (x - 4) 3y + 3 = 2x - 8 2x - 3y - 5 = 0 . . . required equation. Example Find the equation of a straight line through Solution : Using two points form i.e. We get \ 40x + 8 = - 6y + 30 i.e. 40x + 6y - 22 = 0 or 20x + 3y - 11 = 0 . . . required equation. Example Put the equation 3x + 4y + 6 = 0 into the slope intercept form, and find the slope and y-intercept. Solution : 3x + 4y + 6 = 0 4y = - 3x - 6
y = Comparing with y = mx + c, we see that slope m = - 3/4 and y - intercept c = - 3/2 Example Find the x and y intercepts of the straight line 3x + 4y - 12 = 0 and sketch the graph. Solution : 3x + 4y - 12 = 0 3x + 4y = 12 Dividing by 12 throughout
a = 4 (x intercept) and b = 3 (y intercept)
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8.1 Definition |
and (1, -3). 
i.e. 
= 1 Comparing with 
= 1, we get