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Write the equation of the line perpendicular to 2x+3y=9 that passes through (-2,5). Write your answer in slope-intercept form. S

Harman [31]

ANSWER

$y = \frac{3}{2} x + 8$

EXPLANATION

The line given to us has equation,

$2x + 3y = 9$

We need to write this equation in the slope intercept form to obtain,

$3y = - 2x + 9$

$\Rightarrow \: y = - \frac{2}{3}x + 3$

The slope of this line is

$m_1 = - \frac{2}{3}$
Let the slope of the perpendicular line be

$m_2$

Then
$m_1 \times m_2 = - 1$

$- \frac{2}{3} m_2= - 1$

This implies that,

$m_2 = - 1 \times - \frac{3}{2}$

$m_2 = \frac{3}{2}$

Let the equation of the perpendicular line be,

$y = mx + b$

We substitute the slope to get,

$y = \frac{3}{2} x + b$

Since this line passes through
$(-2,5)$
it must satisfy its equation.

This means that,

$5= \frac{3}{2} ( - 2)+ b$

$5 = - 3 + b$

$5 + 3 = b$

$b = 8$

Wherefore the slope-intercept form is

$y = \frac{3}{2} x + 8$

6 0

3 years ago

Which of the following is something that will not affect your homeowners insurance premium? a. the distance of the home from a s

RideAnS [48]

The correct answer for this question above homeowners insurance premium would be option A. The one that is something that will not affect your homeowners insurance premium would be the distance of the home from school. In addition, the color of the home won't affect it as well. Hope this answer helps.

6 0

3 years ago

Read 2 more answers

You are graphing y < 2x + 1. What type of line do you use and where do you shade?

bazaltina [42]

Since there isn't a line under the < sign, this means that we used a dotted or dashed line. The dotted or dashed line indicates that we do NOT include the boundary as part of the solution set.

Since y is isolated and we have a less than sign, this means we shade below the dashed/dotted boundary line. Specifically, the boundary line is the graph of y = 2x+1. This boundary line goes through (0,1) and (1,3). Again, points on this boundary line are NOT part of the solution set.

So in summary we have:
A dashed or dotted boundary line
The shaded region is below the dashed/dotted boundary line.

3 0

3 years ago

The sugar content of the syrup is canned peaches is normally distributed. Assumethe can is designed to have standard deviation 5

andreyandreev [35.5K]

Answer: 0.50477

Step-by-step explanation:

Given : The sugar content of the syrup is canned peaches is normally distributed.

We assume the can is designed to have standard deviation $\sigma=5$ milligrams.