Question

Find an equation of the line that satisfies the given conditions.
Through (-1, -2); perpendicular to the line 2x + 7y + 8 = 0

Answer 1

Answer:

the (-1,-2) is (x,y)

2(-1)+7(-2)+8=0

-2-14+8

-16+8

=8

Answer 2

The equation of the line that satisfies the given conditions is

2y - 7x - 3 = 0

The equation of a line in point-slope form is expressed as;

$y-y_0 =m(x-x_0)$

where;

• m is the slope
• $(x_0,y_0)$ is the point on the line

Given the equation 2x + 7y + 8 = 0

Reqrite in standard form:

2x + 7y + 8 = 0

7y = -2x - 8

y = -2/7 x -8/7

The slope of the line perpendicular = 7/2

Substitute the slope m = 7/2 and point (-1, -2) into the expression above:

$y - (-2) = 7/2(x-(-1))\\y + 2 = 7/2(x+1)\\2(y+2) = 7(x+1)\\2y+4 = 7x+7\\2y - 7x + 4 - 7=0\\2y-7x-3 = 0$

Hence the equation of the line that satisfies the given conditions is

2y - 7x - 3 = 0

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