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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.

User Schmauch
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2 Answers

4 votes

Steps:

  • 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:
    (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:


(-5-(-2))/(4-0)=-(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=-(3)/(4)x-2 . From here we can solve for the standard form.

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


(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

Answer:

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

User AaronMK
by
8.6k points
2 votes

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=(y_2-y_1)/(x_2-x_1)

Substitute:


m=(-2-(-5))/(0-4)=(-2+5)/(-4)=(3)/(-4)=-(3)/(4)

Therefore we have the equation of a line


y=-(3)/(4)x-2

Convert to the standard form:
Ax+By=C


y=-(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}

User Driss NEJJAR
by
8.9k points

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