Question

Find The enution of Straight
line through the point (-6,10)
and (1) Parallel (2)perpendicular
to the line 7x+8y= 5.​

Answer 1

Answer:

Equation of the line which is parallel to line "7x + 8y = 5" is 7x + 8y - 42 = 0.

Equation of the line which is perpendicular to line "7x + 8y = 5" is 8x - 7y + 118 = 0 .

Step-by-step explanation:

Case 1 : line is parallel to 7x + 8y = 5.

From the properties of straight lines

• If two lines are parallel to each other then their slopes are equal.
• If one line is perpendicular to other then the product of their slopes is - 1.

In case 1, lines are parallel to each other, so their slope must be equal.

= > Slope of "7x + 8y = 5" = Slope of line passing through ( - 6 , 10 )

= > - X coefficient / Y coefficient = Slope of line passing through ( - 6 , 10 )

= > - 7 / 8 = Slope of line passing through ( - 6 , 10 ).

From the properties of straight lines

• Slope of straight any line is given by using : y - a = m( x - b ), where ( a , b ) is a point on that line and m is the slope of that line.

Here, the line passes through ( - 6 , 10 ) and its slope of - 7 / 8

Hence,

= > Equation of this line

= > y - 10 = ( - 7 / 8 ) { x - ( - 6 ) }

= > 8( y - 10 ) = - 7( x + 6 )

= > 8y - 80 = - 7x - 42

= > 7x + 8y - 80 + 42 = 0

= > 7x + 8y - 42 = 0

Hence, equation of the line which is parallel to line "7x + 8y = 5" is 7x + 8y - 42 = 0.

Case 2 : Lines are perpendicular to each other.

In case 2, lines are perpendicular to each other, so product of their slopes must be - 1

= > Slope of "7x + 8y = 5" x Slope of line passing through ( - 6 , 10 ) = - 1

= > - X coefficient / Y coefficient of "7x + 8y = 5" = - 1 / Slope of line passing through ( - 6 , 10 )

= > - 7 / 8 = - 1 / slope of line passing through ( - 6 , 10 ).

= > 8 / 7 = Slope of line passing through ( - 6 , 10 ) .

Here, the line passes through ( - 6 , 10 ) and its slope of 8 / 7

Hence,

= > Equation of this line

= > y - 10 = ( 8 / 7 ) { x - ( - 6 ) }

= > 7( y - 10 ) = 8 ( x + 6 )

= > 7y - 70 = 8x + 48

= > 8x - 7y + 118 = 0

Hence, equation of the line which is perpendicular to line "7x + 8y = 5" is 8x - 7y + 118 = 0.