Find the slope of a line perpendicular to the line
y=x
Use the slope-intercept form of a linear equation to write the equation of each line with the given slope and y-intercept.
slope -3; y-intercept (0, -1/5)
write the equation of the line passing through the given points. write the equation in standard form Ax+By=C
(8,-3) AND (4,-8)
Write an equation of each line. Write the equation in the form x=a y=b or y =mx+b
Through (-2,-3): perpendicular to 3x+2y =5
Find the equation of each line. Write the equation in standard form unless indicated otherwise.
Through (3,5) perpendicular to the line 2x-y=8
Solve each system by graphing.
-x +3y =6
3x - 9y = 9
These two are together supposed to have a bracket around them as a whole.
Use the substitution method to slove each system of equation.
x= 3y -1
2x - 6y = -2
These two are together supposed to have a bracket around them as a whole.
Solve each system of equation
1/2x - 1/3y = -3
1/8x + 1/6y =0
These two are together supposed to have a bracket around them as a whole
SOLUTION :
(I)
y = x is a line with slope 1.0 and y-intercept of 0.
Line perpendicular to it will have slope = - 1/1 = - 1.
So, slope of the line perpendicular to line y = x is equal to - 1 (ANSWER).
(ii)
Slope = - 3 and y-intercept point is (0, - 1/5)
So, its equation is :
y = - 3 x - 1/5 (ANSWER).
(iii)
Slope of the line passing through points (8, - 3) and (4, - 8)
= (y2 - y1) / (x2 - x1)
= (- 8 - (- 3)) / (4 - 8)
= (- 5) / (- 4)
= 5/4
So, equation of this line will be : y = 5/4 x + b
As it passes through point (8, - 3). This point should satisfy the above equation.
=> - 3 = 5/4 * 8 + b
=> - 3 = 10 + b
=> b = - 13
Hence, equation of the line will be :
y = 5/4 x - 13
=> 4y = 5 x - 52
=> - 5x + 4y = - 52 (standard form) (ANSWER)
(iv)
3x + 2y = 5
=> 2y = - 3x + 5
=> y = - 3/2 x + 5/2 (slope -intercept form)
Hence, its slope = - 3/2.
Slope of the line perpendicular to it is = - 1 / (- 3/2) = 2/3
Equation of this line : y = 2/3 x + b
It passes through point (- 2, - 3), so this point should satisfy yer equation of the line.
=> - 3 = 2/3 (- 2) + b
=> - 3 = - 4/3 + b
=> b = - 3 + 4/3 = - 5/3
Hence, equation of the line will be : y = 2/3 x - 5/3 (ANSWER).
(v)
2x - y = 8
=> y = 2x - 8
Its slope is = 2
S0, slope of the line perpendicular = - 1/ 2 = - 1/2
So, equation of perpendicular line : y = - 1/2 x + b
As it passes through point (3, 5) ,
=> 5 = - 1/2 * 3 + b
=> b = 5 + 3/2 = 13/2
So, equation of perpendicular line : y = - 1/2 x + 13/2 (ANSWER).
(vi)
Use demos.com.
Write equations - x + 3y = 6 and 3x - 9y = 9 in table 1 and table 2 on the LHS. See the graphs of both the lines on the same grid in different colours. Both the lines are parallel with different y-intercepts.
(vii)
x = 3y - 1
=> x - 3y = - 1 ……… (1)
Second line is :
2x - 6y = - 2 ……… (2)
Eliminate y by (1) * - 2 and add to (2)
=> 0 + 0 = 0
It means equation (1) and (2) are same and both lines represent same line.
Hence infinite solutions exist. (ANSWER).
(viii)
1/2 x - 1/3 y = - 3
Multiply by 6 :
=> 3x - 2y = - 18 ……… (1)
1/8 x + 1/6 y = 0
Multiply by 24 :
=> 3x + 4y = 0 ………. (2)
Eliminate x by (1) - (2);
=> - 6y = - 18
=> y = 3
=> from (1), x = (- 18 + 2(3)) / 3 = - 4
So solution (x, y) is = (- 4, 3) (ANSWER).
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