Respuesta :
The equation parallel to [tex]y = \frac{1}{3}x - 7[/tex] that passes through the point (-2, 5) is [tex]y = \frac{1}{3}x + \frac{17}{3}[/tex]
Solution:
Given that line parallel to [tex]y = \frac{1}{3}x - 7[/tex] that passes through the point (-2, 5)
We have to find the equation of line
Let us first find the slope of line
The slope intercept form is given as:
y = mx + c ------ eqn 1
Where "m" is the slope of line and "c" is the y - intercept
Given equation of line is:
[tex]y = \frac{1}{3}x - 7[/tex] -------- eqn 2
On comparing eqn 1 and eqn 2,
[tex]m = \frac{1}{3}[/tex]
Thus the slope of line "m" = [tex]\frac{1}{3}[/tex]
We know that slope of parallel lines are equal
So slope of line parallel to [tex]y = \frac{1}{3}x - 7[/tex] is also [tex]\frac{1}{3}[/tex]
Now let us find the equation of line with slope [tex]m = \frac{1}{3}[/tex] and passes through point (-2, 5)
Substitute "m" and (x, y) = (-2, 5) in eqn 1
[tex]5 = \frac{1}{3}(-2) + c[/tex]
15 = -2 + 3c
17 = 3c
[tex]c = \frac{17}{3}[/tex]
So the required equation is:
Substitute "m" and "c" value in eqn 1
[tex]y = \frac{1}{3}x + \frac{17}{3}[/tex]
Thus the required equation is found
