Answer:
[tex]y + 1 =-\frac{5}{3}(x-1)[/tex]
[tex]y = -\frac{5}{3}x + \frac{2}{3}[/tex]
Step-by-step explanation:
To write the equation of a line you need a point and a slope. Use the two points given to find the slope.
[tex]m = \frac{-1 - 4}{1--2} = \frac{-5}{3}[/tex]
Substitute m = -5/3 and the point (1,-1) into the point slope form.
[tex]y - y_1 = m(x-x_1)\\y --1 = -\frac{5}{3}(x-1)\\y + 1 =-\frac{5}{3}(x-1)[/tex]
Use the distributive property to convert to slope intercept form.
[tex]y + 1 = -\frac{5}{3}x + \frac{5}{3}\\y = -\frac{5}{3}x + \frac{5}{3} - 1\\y = -\frac{5}{3}x + \frac{2}{3}[/tex]
