Respuesta :
Answer
y = (1/2)x + 5
Step-by-step explanation
Equation of a line in slope-intercept form
[tex]y=mx+b[/tex]where m is the slope and (0, b) is the y-intercept
The slope of the line that passes through the points (x₁, y₁) and (x₂, y₂) is calculated as follows:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]In this case, the line passes through the points (2, 6) and (-2, 4), then its slope is:
[tex]\begin{gathered} m=\frac{4-6}{-2-2}\frac{}{} \\ m=\frac{-2}{-4} \\ m=\frac{1}{2} \end{gathered}[/tex]Substituting with the point (2, 6), that is, x = 2 and y = 6, and m = 1/2 into the general equation, and solving for b:
[tex]\begin{gathered} 6=\frac{1}{2}\cdot2+b \\ 6=1+b \\ 6-1=1+b-1 \\ 5=b \end{gathered}[/tex]Finally, substituting m = 1/2 and b = 5 into the general equation, the equation of this line is:
[tex]y=\frac{1}{2}x+5[/tex]