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 ![y = \frac{-1}{5}x + \frac{16}{5}](https://tex.z-dn.net/?f=y%20%3D%20%5Cfrac%7B-1%7D%7B5%7Dx%20%2B%20%5Cfrac%7B16%7D%7B5%7D)
<h3><u>Solution:</u></h3>
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
<em><u>The slope intercept form is given as:</u></em>
y = mx + c -------- eqn 1
Where "m" is the slope of line and "c" is the y - intercept
<em><u>Let us first find the slope of line</u></em>
Given equation of line is x + 5y = 10
![5y = -x + 10\\\\y = \frac{-1}{5}x + \frac{10}{5}\\\\y = \frac{-1}{5}x + 2](https://tex.z-dn.net/?f=5y%20%3D%20-x%20%2B%2010%5C%5C%5C%5Cy%20%3D%20%5Cfrac%7B-1%7D%7B5%7Dx%20%2B%20%5Cfrac%7B10%7D%7B5%7D%5C%5C%5C%5Cy%20%3D%20%5Cfrac%7B-1%7D%7B5%7Dx%20%2B%202)
On comparing the above equation of line with slope intercept form,
![m = \frac{-1}{5}](https://tex.z-dn.net/?f=m%20%3D%20%5Cfrac%7B-1%7D%7B5%7D)
We know that slopes of parallel lines are equal
So the slope of line parallel to given line is also ![m = \frac{-1}{5}](https://tex.z-dn.net/?f=m%20%3D%20%5Cfrac%7B-1%7D%7B5%7D)
<em><u>Let us find the equation of line with slope m = -1/5 and passes through the point (1, 3)</u></em>
![\text {substitute } m=\frac{-1}{5} \text { and }(x, y)=(1,3) \text { in eqn } 1](https://tex.z-dn.net/?f=%5Ctext%20%7Bsubstitute%20%7D%20m%3D%5Cfrac%7B-1%7D%7B5%7D%20%5Ctext%20%7B%20and%20%7D%28x%2C%20y%29%3D%281%2C3%29%20%5Ctext%20%7B%20in%20eqn%20%7D%201)
![3 = \frac{-1}{5} \times 1 + c\\\\15 = -1 + 5c\\\\16 = 5c\\\\c = \frac{16}{5}](https://tex.z-dn.net/?f=3%20%3D%20%5Cfrac%7B-1%7D%7B5%7D%20%5Ctimes%201%20%2B%20c%5C%5C%5C%5C15%20%3D%20-1%20%2B%205c%5C%5C%5C%5C16%20%3D%205c%5C%5C%5C%5Cc%20%3D%20%5Cfrac%7B16%7D%7B5%7D)
<em><u>Thus the required equation is:</u></em>
![\text {substitute } m=\frac{-1}{5} \text { and } c=\frac{16}{5} \text { in eqn } 1](https://tex.z-dn.net/?f=%5Ctext%20%7Bsubstitute%20%7D%20m%3D%5Cfrac%7B-1%7D%7B5%7D%20%5Ctext%20%7B%20and%20%7D%20c%3D%5Cfrac%7B16%7D%7B5%7D%20%5Ctext%20%7B%20in%20eqn%20%7D%201)
![y = \frac{-1}{5}x + \frac{16}{5}](https://tex.z-dn.net/?f=y%20%3D%20%5Cfrac%7B-1%7D%7B5%7Dx%20%2B%20%5Cfrac%7B16%7D%7B5%7D)
Thus the required equation of line is found