All categories

3 years ago

Find the equation of the line through (8,−6) which is perpendicular to the line y=x3−7.

Mathematics

1 answer:

ycow [4]3 years ago

8 0

Answer:

y = (-1/3)(x + 10)

Step-by-step explanation:

The slope of the new (perpendicular) line is the negative reciprocal of the slope of the given line, which appears to be 3. Thus, the perpendicular line has the slope -1/3.

Using the slope-intercept form y = mx + b, and substituting the givens, we obtain:

y = mx + b => -6 = (-1/3)(8) + b, or

-6 = -8/3 + b. We must solve for the y-intercept, b:

Multiplying all three terms by 3 removes the fraction:

-18 = -8 + 3b. Thus, -10 = 3b, and so b must be -10/3.

The desired equation is

y = (-1/3)x - 10/3, or

y = (-1/3)(x + 10)

You might be interested in

An isosceles triangle has two angles both equal to x°. The third angle is 60° bigger than either of these. Find the value of x°.

Elina [12.6K]

X+x+(x+60)=180
3x+60=180
3x=120
x=40

5 0

4 years ago

HELP PLEASE!!! i do not understand

mel-nik [20]

Answer:

a)-3>-7

b)3>-4 The symbol was preserved.

c)-6<8 The symbol was reversed.

Step-by-step explanation:

Hope this helps! :)

5 0

3 years ago

Can someone pleeeeease help me!!

charle [14.2K]

Answer:

I’m pretty sure it’s 73% but I’m not completely sure

6 0

3 years ago

Find the equation of the line passing through point (4,2) and perpendicular to AB

Setler [38]

Answer:

a. -⅓

b. 3

c. y = 3x - 10

Step-by-step explanation:

a. Gradient of line AB:

A(1, 3), B(7, 1)

$Gradient = \frac{y_2 - y_1}{x_2 - x_1} = \frac{1 - 3}{7 - 1} = \frac{-2}{6} = -\frac{1}{3}$

Gradient (m) = -⅓

b. The of the line that is perpendicular to line AB would be the negative reciprocal of the gradient of line AB.

Thus, the negative reciprocal of -⅓ = 3

Gradient of the line perpendicular to line AB = 3

c. Equation of the line that passes through (4, 2) and is perpendicular to line AB:

We can write the equation using the point-slope form equation, y - b = m(x - a), where,

(a, b) represents a point on the line, and,

m = gradient/slope

We know that the gradient/slope (m) = 3

Also, a point, (a, b) = (4, 2).

Therefore, substitute a = 4, b = 2, and m = 3 into y - b = m(x - a)

Thus:

y - 2 = 3(x - 4)

y - 2 = 3x - 12

Add 2 to both sides

y = 3x - 12 + 2

y = 3x - 10

5 0

3 years ago

Find each sum (-4y+3) + (11y-5)

Airida [17]

Answer:

7y−2

Step-by-step explanation:

8 0

3 years ago