Question

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

Answer 1

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).

Answer 2

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