Answer:
y = 0.5x + 1.5
Explanation:
The equation of a line that passes through two points (x₁, y₁) and (x₂, y₂) can be calculated as:
[tex]y-y_1=m(x-x_1)[/tex]Where m is the slope and it is equal to:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]So, if we replace (x₁, y₁) by (-5, -1) and (x₂, y₂) by (5, 4), we get that the slope is equal to:
[tex]m=\frac{4-(-1)}{5-(-5)}=\frac{4+1}{5+5}=\frac{5}{10}=0.5[/tex]Then, the equation of the line is:
[tex]\begin{gathered} y-(-1)=0.5(x-(-5)) \\ y+1=0.5(x+5) \end{gathered}[/tex]Finally, if we solve for y, we get:
[tex]\begin{gathered} y+1=0.5x+0.5(5) \\ y+1=0.5x+2.5 \\ y+1-1=0.5x+2.5-1 \\ y=0.5x+1.5 \end{gathered}[/tex]So, the equation of the line is:
y = 0.5x + 1.5
