Respuesta :
Answer:
[tex]$ 2x - 3y - 6 = 0$[/tex]
Step-by-step explanation:
When we are to find the equation of the line passing through two points, say [tex]$ (x_1, y_1) $[/tex] and [tex]$ (x_2, y_2) $[/tex] we use the two -point form.
The two point form is as follows:
[tex]$ \frac{y - y_1} {y_2 - y_1} = \frac{x - x_1}{x_2 - x_1} $[/tex]
Here, [tex]$ (x_1 , y_1) = (0 , -2) $[/tex] and [tex]$ (x_2, y_2) = (6 , 0) $[/tex].
Therefore we have: [tex]$ \frac{y + 2}{0 + 2} = \frac{x - 0}{6 - 0} $[/tex]
[tex]$ \implies \frac{y + 2}{1} = \frac{x}{3} $[/tex]
[tex]$ \implies 3y + 6 = x $ $ \implies x -3y + 6 = 0$ [/tex]
Answer:
The equation of the line is [tex]y = \frac{x}{3} - 2[/tex]
Step-by-step explanation:
Given
Point 1 (0, -2)
Point 2 (6, 0).
Required
What is the equation of the line?
To get the equation of the line, we have to calculate the two -point form gradient formula.
Let gradient be represented by m
The expression for m is as follows;
[tex]m = \frac{y - y_{1} }{x - x_{1}}[/tex] and
[tex]m = \frac{y_{2} - y_{1} }{x_{2} - x_{1}}[/tex]
Since m = m, we have
[tex]\frac{y - y_{1} }{x - x_{1}} = \frac{y_{2} - y_{1} }{x_{2} - x_{1}}[/tex]
Such that
[tex]x_{1} = 0, x_{2} = 6, y_{1} = -2, y_{2} = 0[/tex]
By Substituting these values in the expression above, we'll get the equation of the line
[tex]\frac{y - y_{1} }{x - x_{1}} = \frac{y_{2} - y_{1} }{x_{2} - x_{1}}[/tex]
becomes
[tex]\frac{y - (-2) }{x - 0} = \frac{0 - (-2) }{6 - 0}[/tex]
[tex]\frac{y + 2 }{x} = \frac{0 + 2 }{6}[/tex]
[tex]\frac{y + 2 }{x} = \frac{2 }{6}[/tex]
[tex]\frac{y + 2 }{x} = \frac{1}{3}[/tex]
Multiply 3x to both sides
[tex]3x * \frac{y + 2 }{x} = \frac{1}{3} * 3x[/tex]
[tex]3 ( {y + 2 }) = x[/tex]
Open bracket
[tex]3y + 6 = x[/tex]
Make y the subject of formula
[tex]3y = x - 6[/tex]
Divide both sides by 3
[tex]y = \frac{x - 6}{3}[/tex]
[tex]y = \frac{x}{3} - \frac{6}{3}[/tex]
[tex]y = \frac{x}{3} - 2[/tex]
Hence, the equation of the line is [tex]y = \frac{x}{3} - 2[/tex]
