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inysia [295]
3 years ago
6

Question 13

Mathematics
1 answer:
natali 33 [55]3 years ago
7 0

Answer:

y - 7 = (x + 5)

Step-by-step explanation:

Point-slope form: y - y1 = m(x - x1)

Slope(m) = 1

Point: (-5, 7) = (x1, y1)

To write the equation in point-slope form, we need to know the slope and one point. Since we were already given the values of the slope and one point, all we have to do is input those values into the equation:

y - y1 = m(x - x1)

y - 7 = 1(x - (-5))

y - 7 = (x + 5)

The equation in point-slope form is: y - 7 = (x + 5)

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State whether the lines are parallel, perpendicular,or neither.
cluponka [151]

Answer:

Please check the explanation.

Step-by-step explanation:

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  • Two lines are perpendicular if the product of their slope is -1

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

y=mx+b

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Given the lines

1)

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Comparing with y=mx+b, the slope of y = 6х - 3:

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m₁ × m₂ = -1

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2)

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Comparing with y=mx+b, the slope of y = 3x + 2:

m₁=3  

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simplifying to write in slope-intercept form

y=3x-3

Comparing with y=mx+b, the slope of y=3x-3:

m₂=3

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Thus, the lines y = 3x + 2 and 2y = 6x - 6 are paralle.

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  • 8x - 2y = 3

simplifying to write in slope-intercept form

y = 4x - 3/2

Comparing with y=mx+b, the slope of y = 4x - 3/2:

m₁=4  

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simplifying to write in slope-intercept form

y=-1/4x-1/4

Comparing with y=mx+b, the slope of y=-1/4x-1/4:

m₂=-1/4

As

m₁ × m₂ = -1

4 ×  - 1/4 = -1

-1 = -1

Thus, the lines 8x - 2y = 3 and x + 4y = - 1 are perpendicular.

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y = -3/2x + 5/2

Comparing with y=mx+b, the slope of y = -3/2x + 5/2:

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simplifying to write in slope-intercept form

y = -2/3x - 1

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simplifying to write in slope-intercept form

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m₂=6

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Thus, the lines y - 5 = 6x and y - 6x = -1 are paralle.

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m₁=3  

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As m₁ and m₂ are neither equal nor their product is -1, hence the lines neither perpendicular nor parallel.

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