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3 years ago

Determine whether the lines are parallel, intersect, or coincide. y-7x=6, y+7x=8

Mathematics

1 answer:

NikAS [45]3 years ago

3 0

The slope for the first problem given is -7

The slope for the second problem is 7

As these are the same slope and not opposite reciprocals, the lines are neither parallel or perpendicular.

This means that the lines will cross at a point at some point in the graph, meaning that your answer would be that the lines intersect.

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Find the equation of the line that is parallel to the line x + 5y = 10 and passes through the point (1, 3).

Romashka-Z-Leto [24]

The equation of the line that is parallel to the line x + 5y = 10 and passes through the point (1, 3) in slope intercept form is $y = \frac{-1}{5}x + \frac{16}{5}$

<h3>Solution:</h3>

Given that a line is parallel to line x + 5y = 10 and passes through the point (1, 3)

We have to find the equation of line

The slope intercept form is given as:

y = mx + c -------- eqn 1

Where "m" is the slope of line and "c" is the y - intercept

Let us first find the slope of line

Given equation of line is x + 5y = 10

$5y = -x + 10\\\\y = \frac{-1}{5}x + \frac{10}{5}\\\\y = \frac{-1}{5}x + 2$

On comparing the above equation of line with slope intercept form,

$m = \frac{-1}{5}$

We know that slopes of parallel lines are equal

So the slope of line parallel to given line is also $m = \frac{-1}{5}$

Let us find the equation of line with slope m = -1/5 and passes through the point (1, 3)

$\text {substitute } m=\frac{-1}{5} \text { and }(x, y)=(1,3) \text { in eqn } 1$

$3 = \frac{-1}{5} \times 1 + c\\\\15 = -1 + 5c\\\\16 = 5c\\\\c = \frac{16}{5}$

Thus the required equation is:

$\text {substitute } m=\frac{-1}{5} \text { and } c=\frac{16}{5} \text { in eqn } 1$

$y = \frac{-1}{5}x + \frac{16}{5}$

Thus the required equation of line is found

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3 years ago

What is the volume of a hemisphere with a diameter of 51 m, rounded to the nearest tenth of a cubic meter?

tigry1 [53]

Answer:

52,084 m (someone check me on this please)

Step-by-step explanation:

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A number g multiplied by -8 is at least 1/4

Mashcka [7]

G is -0.04 or greater.

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3 years ago

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rusak2 [61]

Answer:

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Step-by-step explanation:

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3 years ago

10 POINTS PLEASE I NEED THIS!!! :) What is the equation in point-slope form of the line that passes through the point (3, −2) an

Reil [10]

Answer: y + 2 = 2/3 (x - 3)

Step-by-step explanation:

1. Point-slope form is y-y1 = m(x - x1)

2. plug in the slope 2/3 for m, -2 for y1, and 3 for x1

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