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3 years ago

The equation of a line in slope-intercept form through the point (3, -4) and had a slope of 6

Mathematics

1 answer:

Ket [755]3 years ago

4 0

Answer:

The equation of a line in slope-intercept form through the point (3, -4) and had a slope of 6 will be:

y = 6x - 22

Step-by-step explanation:

Given

The point = (3, -4)

Slope = m = 6

We know that the slope-intercept form of the line equation

y = mx+b

where

m is the slope

b is the y-intercept

substituting m = 6 and the point (3, -4) in the slope-intercept form of the line equation to determine the y-intercept b

y = mx+b

-4 = 6(3) + b

-4 = 18 + b

switch sides

b = -4 - 18

b = -22

now substituting m = 6 and the b = -22 in the slope-intercept form of the line equation

y = mx+b

y = 6x + (-22)

y = 6x - 22

Therefore, the equation of a line in slope-intercept form through the point (3, -4) and had a slope of 6 will be:

y = 6x - 22

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4 years ago

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Answer:

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Step-by-step explanation:

We are given the following dimensions of the triangular pyramid:

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Height of triangular base = 5.2mm

Base of lateral face (triangular) = 6mm

Height of lateral face (triangular) = 8mm

a) To find Area of base of pyramid:

We know that it is a triangular pyramid and the base is a equilateral triangle. $\text{Area of triangle = } \dfrac{1}{2} \times \text{Base} \times \text{Height} ..... (1)\\$

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b) To find area of one lateral surface:

Base = 6mm

Height = 8mm

Using equation (1) to find the area:

$\Rightarrow \dfrac{1}{2} \times 8 \times 6\\\Rightarrow 24\ mm^{2}$

c) To find the lateral surface area:

We know that there are 3 lateral surfaces with equal height and equal base.

Hence, their areas will also be same. So,

$\text{Lateral Surface Area = }3 \times \text{ Area of one lateral surface}\\\Rightarrow 3 \times 24 = 72 mm^{2}$

d) To find total surface area:

Total Surface area of the given triangular pyramid will be equal to <em>Lateral Surface Area + Area of base</em>

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b) Area of one lateral face = $24\ mm^{2}$

c) Lateral Surface Area = $72\ mm^{2}$

d) Total Surface Area = $87.6\ mm^{2}$

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