Respuesta :
The equation of a line passing through points (x₁, y₁) and (x₂, y₂) is given by:
[tex]\frac{y-y_1}{x-x_1}=\frac{y_2-y_1}{x_2-x_1}[/tex]In this problem, we have:
x₁ = 27
y₁ = 186
x₂ = 67
y₂ = 205
So, we can use those values in the above formula to find the equation of the line:
[tex]\begin{gathered} \frac{y-186}{x-27}=\frac{205-186}{67-27} \\ \\ \frac{y-186}{x-27}=\frac{19}{40} \end{gathered}[/tex]Now, we can multiply both sides of the equation by the factor (x - 27):
[tex]\begin{gathered} \frac{y-186}{x-27}(x-27)=\frac{19}{40}(x-27) \\ \\ y-186=\frac{19}{40}x-\frac{513}{40} \end{gathered}[/tex]Finally, the equation in slope-intercept form requires y to be isolated on one side of the equation. So, we need to add 186 to both sides to put the equation in this form:
[tex]\begin{gathered} y-186+186=\frac{19}{40}x-\frac{513}{40}+186 \\ \\ y=\frac{19}{40}x+\frac{-513+186\cdot40}{40} \\ \\ y=\frac{19}{40}x+\frac{7440-513}{40} \\ \\ y=\frac{19}{40}x+\frac{6927}{40} \\ \\ y=0.475x+173.175 \end{gathered}[/tex]Notice you can write the slope and the intercept of the equation using fractions or decimal form.
The slope is the number multiplying x (0.475), while the y-intercept is the constant 173.175.
Therefore, the equation of the line that passes through (27,186) and (67,205) in slope-intercept form is
[tex]y=0.475x+173.175[/tex]