Respuesta :
The equation of the line that is parallel to the line x + 5y = 10 and passes through the point (1, 3) in slope intercept form is [tex]y = \frac{-1}{5}x + \frac{16}{5}[/tex]
Solution:
Given that a line is parallel to line x + 5y = 10 and passes through the point (1, 3)
We have to find the equation 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
Let us first find the slope of line
Given equation of line is x + 5y = 10
[tex]5y = -x + 10\\\\y = \frac{-1}{5}x + \frac{10}{5}\\\\y = \frac{-1}{5}x + 2[/tex]
On comparing the above equation of line with slope intercept form,
[tex]m = \frac{-1}{5}[/tex]
We know that slopes of parallel lines are equal
So the slope of line parallel to given line is also [tex]m = \frac{-1}{5}[/tex]
Let us find the equation of line with slope m = -1/5 and passes through the point (1, 3)
[tex]\text {substitute } m=\frac{-1}{5} \text { and }(x, y)=(1,3) \text { in eqn } 1[/tex]
[tex]3 = \frac{-1}{5} \times 1 + c\\\\15 = -1 + 5c\\\\16 = 5c\\\\c = \frac{16}{5}[/tex]
Thus the required equation is:
[tex]\text {substitute } m=\frac{-1}{5} \text { and } c=\frac{16}{5} \text { in eqn } 1[/tex]
[tex]y = \frac{-1}{5}x + \frac{16}{5}[/tex]
Thus the required equation of line is found
