Answer :
Answer:
[tex]y = -\frac{2}{5}x -\frac{1}{5}[/tex]
Step-by-step explanation:
Given
Passes through: [tex](2,-1)[/tex]
Parallel to: [tex]2x + 5y = 15[/tex]
Required
First, calculate the slope of the parallel line
[tex]2x + 5y = 15[/tex]
Make y the subject
[tex]5y = 15 - 2x[/tex]
Divide through by 5
[tex]y = 3 - \frac{2}{5}x[/tex]
[tex]y =- \frac{2}{5}x+3[/tex]
An equation in slope intercept has the form:
[tex]y = mx + b[/tex]
Where:
m = slope
[tex]y = mx + b[/tex]
So:
[tex]m = -\frac{2}{5}[/tex]
The required is parallel to [tex]2x + 5y = 15[/tex].
This mean, the same slope
The equation is the calculated using:
[tex]y - y_1 = m(x - x_2)[/tex]
This gives:
[tex]y - (-1) = -\frac{2}{5}(x - 2)[/tex]
[tex]y +1 = -\frac{2}{5}x +\frac{2}{5}*2[/tex]
[tex]y +1 = -\frac{2}{5}x +\frac{4}{5}[/tex]
[tex]y = -\frac{2}{5}x +\frac{4}{5}-1[/tex]
Take LCM
[tex]y = -\frac{2}{5}x +\frac{4-5}{5}[/tex]
[tex]y = -\frac{2}{5}x -\frac{1}{5}[/tex]
i.e.
[tex]y = -2/3x -1/5[/tex]