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

Given:

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.

Slope:

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 $m=-\frac{3}{2}$

Equation of the line:

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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8) Tammy uses 1 3/4 cups of laundry detergent per load. When she was finished

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Tammy uses 1 3/4 cups of laundry detergent. The number of loads is 4

Solution:

Given that, Tammy uses 1 3/4 cups of laundry detergent per load.

When she was finished doing laundry one day.

She noticed that she had used 7 cups of laundry detergent.

We have to find how many loads did she do?

Now, we know that, Total cups used can be written as:

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$\begin{array}{l}{\text { Then, number of loads } \times 1 \frac{3}{4}=7} \\\\ {\text { Number of loads } \times \frac{1 \times 4+3}{4}=7} \\\\ {\text { Number of loads } \times \frac{7}{4}=7} \\\\ {\text { Number of loads }=7 \times \frac{4}{7}=4}\end{array}$