A linear equation in the slope-intercep form is y = mx + b.
To find the equation, follow the steps below.
Step 01: Substitute the point (0, 10) in the equation.
[tex]\begin{gathered} y=mx+b \\ 10=m\cdot0+b \\ 10=b \end{gathered}[/tex]Then,
[tex]y=mx+10[/tex]Step 02: Substitute the point (-5, 0).
[tex]0=-5m+10[/tex]Subtract 10 from both sides:
[tex]\begin{gathered} 0-10=-5m+10-10 \\ -10=-5m \end{gathered}[/tex]And divide both sides by -5:
[tex]\begin{gathered} \frac{-10}{-5}=\frac{-5}{-5}m \\ 2=m \end{gathered}[/tex]Step 03: Write the linear equation.
[tex]y=2x+10[/tex]Answer:
[tex]y=2x+10[/tex]