Respuesta :
2x - 3y = 8 is the equation of the line that passes through the point (1,-2) and is parallel to the line passing through the point (-2,-1) and (4,3)
Solution:
We have to find the equation of the line that passes through the point (1, -2) and is parallel to the line passing through the point (-2, -1) and (4, 3)
Let us first find the slope of line
We know slope of a line and slope of line parallel to it are equal
So we can find the slope of line passing thorugh the point (-2, -1) and (4, 3)
The slope of line is given as:
[tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
The points are (-2, -1) and (4, 3)
[tex](x_1, y_1) = (-2, -1)\\\\(x_2,y_2) = (4, 3)[/tex]
Substituting the values we get,
[tex]m = \frac{3-(-1)}{4-(-2)}\\\\m = \frac{4}{6}\\\\m = \frac{2}{3}[/tex]
Thus the slope of line passing thorugh the point (-2, -1) and (4, 3) is [tex]m = \frac{2}{3}[/tex]
So the slope of line parallel to it also [tex]m = \frac{2}{3}[/tex]
Now find the equation of the line that passes through the point (1, -2) with slope [tex]m = \frac{2}{3}[/tex]
The equation of line in slope intercept form is given as:
y = mx + c ---- eqn 1
Where "m" is the slope of line and c is the y - intercept
Substitute (x, y) = (1, -2) and [tex]m = \frac{2}{3}[/tex] in eqn 1
[tex]-2 = \frac{2}{3}(1) + c\\\\-2 = \frac{2+3c}{3}\\\\2 + 3c = -6\\\\3c = -8\\\\c = \frac{-8}{3}[/tex]
[tex]\text{ Substitute } m = \frac{2}{3} \text{ and } c = \frac{-8}{3} \text{ in eqn 1 }[/tex]
[tex]y = \frac{2}{3}x-\frac{8}{3}[/tex]
Writing in standard form, we get
[tex]y = \frac{2x-8}{3}\\\\3y = 2x - 8\\\\2x -3y = 8[/tex]
Thus the equation of line is found
