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Write the equation of a line perpendicular to y = 3x - 8 and that passes through the point (-3, -9)

y + 9 = $- \frac{1}{3}$ (x + 3)
y - 9 = $- \frac{1}{3}$ (x - 3)
y + 9 = -3(x + 3)
y - 9 = 3(x - 3)

hint Hint:

We are given an equation of line. We have to find the equation of line that is perpendicular to the given line and passing through point (-3,-9). We will use the properties of perpendicular lines to solve the question.

The correct answer is: y + 9 = $negative 1 third$ (x + 3)

The given equation of line is y = 3x - 8
We have to find line perpendicular to this line.
Perpendicular lines have a slope that are negative reciprocals each other.
To find the slope of the given line, we will compare the equation with slope-intercept form. The slope-intercept form of a line is y = mx + c. Here m is the slope of the line and c is the y-intercept.
Comparing the given equation of line with slope-intercept form we get,
m = 3
So, our new line will have slope
$m subscript 1 space equals space minus 1 over m m subscript 1 space equals negative 1 third$
Now, we have a point through which line is passing and slope. We will use slope-point form to find the perpendicular line.
Slope-point form is (y – y₁) = m1(x – x₁). Here y1 and X1 are the points through which line is passing. (x₁,y₁) ≡ (-3, -9)
Substituting all the values
$left parenthesis y space minus y right parenthesis space equals space m left parenthesis x space minus space x right parenthesis left square bracket y space minus space left parenthesis negative 9 right parenthesis right square bracket space equals space minus 1 half left square bracket x space minus left parenthesis negative 3 right parenthesis right square bracket y space plus space 9 space equals space minus 1 half left parenthesis x space plus space 3 right parenthesis$
Therefore, the equation of line perpendicular to given line and passing through point (-3,-9) is $y space plus space 9 space equals negative 1 half left parenthesis x space plus space 3 right parenthesis$ .

For such questions, we should know different formulas required to find lines. We should also know the concept of slope of different lines.

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Write the equation of a line perpendicular to y = 3x - 8 and that passes through the point (-3, -9)

y + 9 = (x + 3)y - 9 = (x - 3)y + 9 = -3(x + 3)y - 9 = 3(x - 3)

We are given an equation of line. We have to find the equation of line that is perpendicular to the given line and passing through point (-3,-9). We will use the properties of perpendicular lines to solve the question.

The correct answer is: y + 9 = (x + 3)

Related Questions to study

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A potter is selling vases. The function gives the total profit p(x) , in dollars, the potter will receive if the vases are sold at a price of x dollars each. The graph of y = p(x) is shown.What equation represents the relationship between the price of one vase and the profit?

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y + 9 = $- \frac{1}{3}$ (x + 3)
y - 9 = $- \frac{1}{3}$ (x - 3)
y + 9 = -3(x + 3)
y - 9 = 3(x - 3)

The correct answer is: y + 9 = $negative 1 third$ (x + 3)

As of 2016, there were 118 known elements. These elements can be described with 10 classifications as summarized in the given table.

The percentage of the 10 classifications that have 11 or more elements is $p straight percent sign$ . What is the value of p ?

As of 2016, there were 118 known elements. These elements can be described with 10 classifications as summarized in the given table.

The percentage of the 10 classifications that have 11 or more elements is $p straight percent sign$ . What is the value of p ?

The expression 3xy(2y + 3) is equivalent to $b x y squared plus 9 x y$ , where b is a constant. What is the value of b ?

The expression 3xy(2y + 3) is equivalent to $b x y squared plus 9 x y$ , where b is a constant. What is the value of b ?

$left parenthesis x plus 3 right parenthesis squared plus left parenthesis y minus 7 right parenthesis squared equals 100$
In the xy-plane, the graph of the given equation is a circle. Which point (x , y) lies on the circle?

$left parenthesis x plus 3 right parenthesis squared plus left parenthesis y minus 7 right parenthesis squared equals 100$
In the xy-plane, the graph of the given equation is a circle. Which point (x , y) lies on the circle?

$y equals 1 half x plus 5$
One of the two equations in a linear system is given. The system has no solution. Which equation could be the second equation in this system?

$y equals 1 half x plus 5$
One of the two equations in a linear system is given. The system has no solution. Which equation could be the second equation in this system?

A potter is selling vases. The function gives the total profit p(x) , in dollars, the potter will receive if the vases are sold at a price of x dollars each. The graph of y = p(x) is shown.

What equation represents the relationship between the price of one vase and the profit?

A potter is selling vases. The function gives the total profit p(x) , in dollars, the potter will receive if the vases are sold at a price of x dollars each. The graph of y = p(x) is shown.

What equation represents the relationship between the price of one vase and the profit?