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CAN SOMEONE PLLSSS HELP ME WITH THIS PROBLEM

CAN SOMEONE PLLSSS HELP ME WITH THIS PROBLEM-example-1
User David Cram
by
8.4k points

1 Answer

3 votes

Answer:


y = 3x - 5

Explanation:

We can write the equation of the line we are trying to solve for in point-slope form, then convert it to slope-intercept form.

Point-slope form is:


y - b = m(x - a)

where
m is the line's slope and
(a, b) is a point on the line.

We are given in the problem that
(2, 1) is a point on the line, so we can identify the following variables to plug into point-slope form:


  • a = 2

  • b = 1

We know that a slope that is perpendicular to a given slope is its negative reciprocal. In equation form:


m_\perp = -(1)/(m)

We can find this for
m = -1/3 :


m_\perp = -\frac{\text{ }1\text{ }}{-(1)/(3)}

↓ skip, flip, and multiply


m_\perp = -1 \cdot \left(-\frac{3}1\right)


m_\perp = 3

Now that we have
a,
b, and
m, we can find an equation for the line perpendicular to
y=-(1)/(3)x + 2 that goes through
(2, 1) by plugging these values into the point-slope form equation:


y - b = m_\perp(x - a)


y - 1 = 3(x - 2)

Finally, we can convert this to slope-intercept form by isolating
y.


y - 1 = 3(x - 2)

↓ apply the distributive property to the right side ...
a(b + c) = ab + ac


y - 1 = 3x - 6

↓ add 1 to both sides


\boxed{y = 3x - 5}

User Silambarasan
by
8.0k points

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