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Line CD passes through points C(3, –5) and D(6, 0). What is the equation of line CD in standard form?
1. 5x + 3y = 18
2. 5x – 3y = 30
3. 5x – y = 30
4. 5x + y = 18

Respuesta :

Rinkhals

Line CD is Passing through the Points (3 , -5) and (6 , 0)

Slope of a Line Passing through two points (x₁ , y₁) and (x₂ , y₂) is given by :

[tex]\heartsuit\;Slope(m) = \frac{y_1 - y_2}{x_1 - x_2}[/tex]

here x₁ = 3 and x₂ = 6 and y₁ = -5 and y₂ = 0

[tex]\heartsuit\;Slope(m) = \frac{-5 - 0}{3 - 6} = \frac{-5}{-3} = \frac{5}{3}[/tex]

We know that the form of line passing through point (x₀ , y₀) and having slope m is : y - y₀ = m(x - x₀)

Here the line passes through the point (3 , -5) and (6 , 0)

We can take any one point of the both

let us take (3 , -5)

x₀ = 3 and y₀ = -5 and we found [tex]m = \frac{5}{3}[/tex]

Equation of the line : [tex]y + 5 = \frac{5}{3}(x - 3)[/tex]

⇒ 3y + 15 = 5x - 15

⇒ 5x - 3y = 30

Option 2 is the Answer

adioabiola

The equation of the line CD expressed in standard form which passes through the points C(3, –5) and D(6, 0) is;. 5x - 3y = 30

The equation of a straight line can be determined by first determining the slope of the line if two points are given on the straight line.

  • Therefore, slope, m = (y2 - y1)/(x2 - x1)

  • slope, m = {0 - (-5)}/(6 - 3)

m = 5/3.

The equation of the line can then be gotten from the slope and a pair of ordinates as follows;

  • m = 5/3 = (y-0)/(x - 6)

  • 5/3 = y/(x - 6)

  • By cross product;we have;

  • 3y = 5x - 30

5x - 3y = 30.

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