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Sagot :
Slope-intercept form:
y = mx + b
where m is the slope and b the y-intercept
3. if two lines are parallel, then they have the same slope. In
y = 6x - 3
the slope is 6, then m = 6
If the line passes through (1,7), then it satisfies the next equation:
7 = 6*1 + b
7 - 6 = b
1 = b
Then, the equation is: y = 6x + 1
4. If two lines are perpendicular then the multiplication of their slopes is equal to -1. In y = 5x + 1, the slope is 5, then:
5*m = -1
m = -1/5
The line passes through (3,-2), that is, when x = 3, y = -2. Replacing these values into the general equation, we get:
y = mx + b
-2 = (-1/5)*3 + b
-2 = -3/5 + b
-2 + 3/5 = b
-1.4 = b
Then, the equation is: y = -1/5x - 1.4
5. To get the slope of 3x + 2y = 8 , we have to isolate y, as follows:
3x + 2y = 8
2y = 8 - 3x
y = (8 - 3x)/2
y = 8/2 - 3/2x
y = 4 - 3/2x
so, its slope is -3/2
The slope of the new line is:
m*(-3/2) = -1
m = (-1)*(-2/3)
m = 2/3
The line passes through (9,4), that is, when x = 9, y = 4. Replacing these values into the general equation, we get:
y = mx + b
4 = 2/3*9 + b
4 = 6 + b
4 - 6 = b
-2 = b
Then, the equation is: y = 2/3x - 2
6. In y = 3/5x + 1, the slop is 3/5. Then, the slope of the new line is:
m*3/5 = -1
m = (-1)*5/3
m = -5/3
The line passes through ( 3,-2), then:
-2 = (-5/3)*3 + b
-2 = -5 + b
-2 + 5 = b
3 = b
Then, the equation is: y = -5/3x + 3
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