Answer:
[tex]\huge\boxed{y=\dfrac{1}{2}x+\dfrac{5}{2}}[/tex]
Step-by-step explanation:
The formula of a slope:
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
We have two points (-9, -2) and (1, 3).
Substitute:
[tex]m=\dfrac{3-(-2)}{1-(-9)}=\dfrac{5}{10}=\dfrac{1}{2}[/tex]
The point-slope form of an equation of a line:
[tex]y-y_1=m(x-x_1)[/tex]
For (-9, -2):
[tex]y-(-2)=\dfrac{1}{2}(x-(-9))\\\\y+2=\dfrac{1}{2}(x+9)[/tex]
For (1, 3):
[tex]y-3=\dfrac{1}{2}(x-1)[/tex]
The slope-intercept form of an equation of a line:
[tex]y=mx+b[/tex]
b - y-intercept
Put the coordinates of the point (1, 3) and the value of a slope to the equation of a line:
[tex]3=\dfrac{1}{2}\cdot1+b\\\\3=\dfrac{1}{2}+b\qquad\text{subtract}\ \dfraC{1}{2}\ \text{from both sides}\\\\2\dfrac{1}{2}=b\to b=\dfrac{5}{2}[/tex]
The equation of a line in the slope-intercept form is:
[tex]y=\dfrac{1}{2}x+\dfrac{5}{2}[/tex]
