URGENT MATH HELP

Question

The equation of a line A is given by     .   Write an equation of a line that is perpendicular to line A and passes through the point (-2,7).

 

y =                   x +  

Answer 1

Using the equation given the perpendicular line would have a slope of -2, the negative reciprocal. This means m=-2, x=-2 and y=7. Use the point slope formula to find the equation. y-y₁=m(x-x₁)

y-y₁=m(x-x₁) Plug in values

y-7=-2(x-(-2)) Simplify the subtraction

y-7=-2(x+2) Distribute to clear the parenthesis

y-7=-2x-4 Add 7 to both sides

y-7+7=-2x-4+7 Simplify

y=-2x+3

Answer 2

Hi Chelsea,

Perpendicular means that the slope is going to be the negative reciprocal of the original slope.

Basically flip the slope and make it negative

So 1/2 becomes -2

Now let's make the new equation with m = -2

y = mx + b

y = -2x + b

Now let's find the y-intercept or b:

plug in (-2,7) for x and y

7 = -2(-2) + b

7 = 4 + b

3 = b

Now rewrite the equation with m and b

y = -2x + 3

Answer 3

First, recall that two lines that are perpendicular to each other have slopes that are opposite reciprocals. Meaning, if one slope is 3/4, the other is - 4/3.

In your case, the line y = 1/2 x + 5 has m = 1/2. Which means that m_⊥ = -2.

Now, you have m = - 2 and the point (-2, 7) so,

y = mx + b

y = -2x + b <-----we don't know what the y - intercept is yet, so we don't know what b is yet.

However, we do know that the point (x, y) = (-2, 7). Thus, we can substitute x = -2 and y = 7

7 = -2(-2) + b (and now solve for b)

7 = 4 + b

b = 3

Thus,

y = -2x + 3

Hope this helps

Mr. K