Respuesta :

gmany

The slope-intercept form:

[tex]y=mx+b[/tex]

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:

[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]

Substitute:

[tex]m=\dfrac{-2-(-5)}{0-4}=\dfrac{-2+5}{-4}=\dfrac{3}{-4}=-\dfrac{3}{4}[/tex]

Therefore we have the equation of a line

[tex]y=-\dfrac{3}{4}x-2[/tex]

Convert to the standard form: [tex]Ax+By=C[/tex]

[tex]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}[/tex]

GoddessofDork

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: [tex]\frac{y_2-y_1}{x_2-x_1}[/tex] 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:

[tex]\frac{-5-(-2)}{4-0}=-\frac{3}{4}[/tex]

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 [tex]y=-\frac{3}{4}x-2[/tex] . From here we can solve for the standard form.

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

[tex]\frac{3}{4}x+y=-2[/tex]

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:

[tex]3x+4y=-8[/tex]

Answer:

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

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