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Lostsunrise [7]
2 years ago
15

Write the equation of a line that passes through the points (0, -2) and (4, -5). Answer MUST be in standard form: Ax + By = C.

Mathematics
2 answers:
Ede4ka [16]2 years ago
7 0
<h2>Steps:</h2>
  • Slope-Intercept Form: y = mx + b (m = slope, b = y-intercept)
  • Standard Form: Ax + By = C (A, B, & C are integers and A must be non-negative)
  • Slope Formula: \frac{y_2-y_1}{x_2-x_1} where (x₁,y₁) and (x₂,y₂) are coordinates.

So for this, I will be putting the equation into slope-intercept form then rearranging it into standard form. Firstly, we need to solve for the slope. To do this, take the 2 coordinates given to us and solve as such:

\frac{-5-(-2)}{4-0}=-\frac{3}{4}

Now, one of the coordinates given to us is (0,-2), which is the y-intercept. With all this info, our slope-intercept equation is y=-\frac{3}{4}x-2 . From here we can solve for the standard form.

Firstly, add 3/4x onto both sides of the equation:

\frac{3}{4}x+y=-2

Now, it may appear that we are finished. However, 3/4 is not an integer (Integers are whole numbers). To make it an integer, we need to multiply both sides by 4:

3x+4y=-8

<h2>Answer:</h2>

<u>In short, the standard form of this equation is 3x + 4y = -8.</u>

shutvik [7]2 years ago
6 0

The slope-intercept form:

y=mx+b

m - slope

b - y-intercept → (0, b).

We have the points (4, -5) and (0, -2) → y-intercept → b = -2.

The formula of a slope:

m=\dfrac{y_2-y_1}{x_2-x_1}

Substitute:

m=\dfrac{-2-(-5)}{0-4}=\dfrac{-2+5}{-4}=\dfrac{3}{-4}=-\dfrac{3}{4}

Therefore we have the equation of a line

y=-\dfrac{3}{4}x-2

Convert to the standard form: Ax+By=C

y=-\dfrac{3}{4}x-2\qquad\text{multiply both sides by 4}\\\\4y=-3x-8\qquad\text{add 3x to both sides}\\\\\boxed{3x+4y=-8}

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Answer:

  750 < p < 1500

Step-by-step explanation:

The total cost of the affair for p attendees is ...

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The average cost is that number divided by p. The answer choices suggest that "between" means that the cost per person cannot be 2.75 or 3.25. Applying the limits to the average cost, we get ...

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_____

* Taking the reciprocals of numbers with the same sign reverses their order:

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An alternate approach to the solution would be to multiply by p:

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