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3 years ago

Which equation represents the line that passes through (–6, 7) and (–3, 6)?

Mathematics

1 answer:

Softa [21]3 years ago

5 0

Answer:

The equation that represents the line that passes through (-6,7) and (-3,6) is: y = -1/3x + 5

Step-by-step explanation:

The equation of line for point=slope form is

y-y₁ = m(x-x₁)

Finding Slope m:

m= y₂-y₁/x₂-x₁

here y₂= 6,y₁= 7,x₂= -3,x₁= -6

m = 6-7/-3-(-6)

m = -1/-3+6

m = -1/3

The slope m = -1/3 and considering point (-6,7) the equation is:

y-y₁ = m(x-x₁)

y-7 = (-1/3)(x-(-6))

y-7 = -1/3(x+6)

y-7 = -1/3x -2

y = -1/3x-2+7

y = -1/3x + 5

So, the equation that represents the line that passes through (-6,7) and (-3,6) is: y = -1/3x + 5

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3 years ago

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3 years ago

Lindsie is painting on a canvas with dimensions of 3 ft by 4 ft. She wants to make a display model for a gallery that has twice

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Answer:

B. 1.4 feet

Step-by-step explanation:

Let, the amount of increase be 'x' ft.

Since, the length and width of the canvas are 4 ft and 3 ft respectively.

Thus, area of the canvas, $A_{c}$ = length × breadth = 4 × 3 = 12 ft²

Since, the area of display model is twice the area of the canvas. We have,

$A_{d}$ = 2 × $A_{c}$

i.e. $A_{d}$ = 2 × 12

i.e. $A_{d}$ = 24 ft².

As, the length and width of the canvas are increased by 'x'.

The, length and width of the display model are (x+4) ft and (x+3) ft.

So, we get,

$A_{c}$ = length × breadth = (x+4) × (x+3) = $x^{2} +7x+12$

Since, $A_{d}$ = 24 ft²

i.e. $x^{2} +7x+12$ = 24

i.e. $x^{2} +7x-12=0$

Solving the quadratic equation, we get,

i.e. x = -8.4 and x= 1.4

Since, the value of x cannot be negative.

Thus, x = 1.4 feet.

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3 years ago