Answer:
[tex]y+5 = \frac{1}{15}(x - 3)}[/tex]
Step-by-step explanation:
Given
[tex]m = \frac{1}{15}[/tex] -- Slope
[tex](x_1,y_1) = (3,-5)[/tex] --- Point
Required
Write an equation in point slope form
The point slope form of an equation is:
[tex]y - y_1 = m(x - x_1)[/tex]
Substitute values for y1, x1 and m
[tex]y-(-5) = \frac{1}{15}(x - 3)}[/tex]
[tex]y+5 = \frac{1}{15}(x - 3)}[/tex]
Hence, the equation in point slope form is:
[tex]y+5 = \frac{1}{15}(x - 3)}[/tex]
Solving further to represent the equation in slope-intercept form, we have:
[tex]y+5 = \frac{1}{15}(x - 3)}[/tex]
[tex]y+5 = \frac{1}{15}x - \frac{1}{15}*3[/tex]
[tex]y+5 = \frac{1}{15}x - \frac{1}{5}[/tex]
Make y the subject
[tex]y= \frac{1}{15}x - \frac{1}{5}-5[/tex]
[tex]y= \frac{1}{15}x - (\frac{1}{5}+5)[/tex]
[tex]y= \frac{1}{15}x - (\frac{1+25}{5})[/tex]
[tex]y= \frac{1}{15}x - (\frac{26}{5})[/tex]
[tex]y= \frac{1}{15}x - \frac{26}{5}[/tex]
