Answer:
[tex]\displaystyle y=\frac{4}{5}x+\frac{13}{5}[/tex]
Step-by-step explanation:
The equation of the line in slope-intercept form is:
y=mx+b
Where m the slope of the line and b the y-intercept.
When two points are given, it's convenient to calculate the slope first.
Suppose we know the line passes through points A(x1,y1) and B(x2,y2). The slope can be calculated with the equation:
[tex]\displaystyle m=\frac{y_2-y_1}{x_2-x_1}[/tex]
The points are (3,5) and (-2,1):
[tex]\displaystyle m=\frac{1-5}{-2-3}=\frac{4}{5}[/tex]
The equation is now:
[tex]\displaystyle y=\frac{4}{5}x+b[/tex]
To calculate b, we use any of the given points and solve for b. Use (3,5):
[tex]\displaystyle 5=\frac{4}{5}3+b[/tex]
Operate:
[tex]\displaystyle 5=\frac{12}{5}+b[/tex]
Solve:
[tex]\displaystyle b=5-\frac{12}{5}=\frac{13}{5}[/tex]
The required equation of the line is:
[tex]\boxed{\displaystyle y=\frac{4}{5}x+\frac{13}{5}}[/tex]
