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Ilia_Sergeevich [38]
3 years ago
15

What is an equation of a line which passes through (6,9) and is perpendicular to the line whose equation is 4x − 6y = 15?

Mathematics
1 answer:
Svetllana [295]3 years ago
3 0

<u>Given:</u>

The equation of the line passes through the point (6,9) and is perpendicular to the line whose equation is 4 x-6 y=15

We need to determine the equation of the line.

<u>Slope</u>:

Let us convert the equation to slope - intercept form.

-6 y=15-4x

   y=\frac{2}{3}x-\frac{5}{2}

From the above equation, the slope is m_1=\frac{2}{3}

Since, the lines  are perpendicular, the slope of the line can be determined using the formula,

m_1 \cdot m_2=-1

  \frac{2}{3} \cdot m_2=-1

      m_2=-\frac{3}{2}

Therefore, the slope of the equation is m=-\frac{3}{2}

<u>Equation of the line:</u>

The equation of the line can be determined using the formula,

y-y_1=m(x-x_1)

Substituting the point (6,9) and the slope m=-\frac{3}{2} in the above formula, we get;

y-9=-\frac{3}{2}(x-6)

Simplifying the terms, we get;

2(y-9)=-3(x-6)

2y-18=-3x+18

3x+2y=36

Thus, the equation of the line is 3x+2y=36

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