Answer:
y = x - 13
Explanation:
The equation of a line that passes through two points (x1, y1) and (x2, y2) is:
[tex]y-y_1=m(x-x_1)[/tex]
Where m is calculated as:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
So, replacing (x1, y1) by (9, -4) and (x2, y2) by (10, -3), we get that m is equal to:
[tex]m=\frac{-3-(-4)}{10-9}=\frac{-3+4}{1}=\frac{1}{1}=1[/tex]
Then, the equation of the line is:
[tex]\begin{gathered} y-(-4)=1(x-9) \\ y+4=x-9 \end{gathered}[/tex]
Finally, to write the equation in slope-intercept form, we need to solve for y, so:
[tex]\begin{gathered} y+4-4=x-9-4 \\ y=x-13 \end{gathered}[/tex]
So, the answer is:
y = x - 13
