Answer:
[tex]\huge\boxed{y=\dfrac{7}{15}x-\dfrac{17}{15}}[/tex]
Step-by-step explanation:
The slope-intercept form of an equation of a line:
[tex]y=mx+b[/tex]
m - slope
b - y-intercept
The formula of a slope:
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
We have two points:
[tex]\left(1,\ -\dfrac{2}{3}\right),\ (-4,\ 3)[/tex]
Substitute:
[tex]m=\dfrac{-3-\left(-\frac{2}{3}\right)}{-4-1}=\dfrac{-\frac{9}{3}+\frac{2}{3}}{-5}=\dfrac{-\frac{7}{3}}{-5}=\dfrac{7}{3}\cdot\dfrac{1}{5}=\dfrac{7}{15}[/tex]
Substitute the value of the slope and coordinates of the second point to the equation of a line:
[tex]-3=\dfrac{7}{15}(-4)+b\\\\-3=-\dfrac{28}{15}+b\qquad\text{add}\ \dfrac{28}{15}\ \text{to both sides}\\\\-\dfrac{45}{15}+\dfrac{28}{15}=-\dfrac{28}{15}+\dfrac{28}{15}+b\\\\-\dfrac{17}{15}=b[/tex]
Finally:
[tex]y=\dfrac{7}{15}x-\dfrac{17}{15}[/tex]
