Answer:
[tex]\displaystyle y=\frac{3}{5}x-1[/tex]
Step-by-step explanation:
The Equation of a Line
The equation of the line in slope-intercept form is:
[tex]y=mx+b[/tex]
Where m is the slope and b the y-intercept.
The equation of a line passing through points (x1,y1) and (x2,y2) can be found as follows:
[tex]\displaystyle y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]
We are given the points (5,2) and (0,-1), thus:
[tex]\displaystyle y-2=\frac{-1-2}{0-5}(x-5)[/tex]
Operating:
[tex]\displaystyle y-2=\frac{-3}{-5}(x-5)[/tex]
[tex]\displaystyle y-2=\frac{3}{5}(x-5)[/tex]
To find the slope-intercept form, we continue to simplify the expression:
Removing the parentheses:
[tex]\displaystyle y-2=\frac{3}{5}x-\frac{3}{5}\cdot 5[/tex]
[tex]\displaystyle y-2=\frac{3}{5}x-3[/tex]
Adding 2:
[tex]\displaystyle y=\frac{3}{5}x-3+2[/tex]
[tex]\mathbf{\displaystyle y=\frac{3}{5}x-1}[/tex]
