Answer:
y = [tex]-\frac{1}{3}x-\frac{2}{3}[/tex]
Step-by-step explanation:
Let the equation of the line is,
y = mx + b
m = Slope of the line
b = y-intercept
Since, slope of a line passing through two points [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] is given by,
m = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
Since, the given line passes through two points (-5, 1) and (4, -2)
Slope of the line 'm' = [tex]\frac{1+2}{-5-4}[/tex] = [tex]-\frac{1}{3}[/tex]
Equation of the line will be,
y = [tex]-\frac{1}{3}x+b[/tex]
Since, this line passes through (4, -2),
-2 = [tex]-\frac{4}{3}+b[/tex]
b = [tex]\frac{4}{3}-2[/tex]
b = [tex]-\frac{2}{3}[/tex]
Therefore, equation of the line will be,
y = [tex]-\frac{1}{3}x-\frac{2}{3}[/tex]
