Respuesta :
The equation of the line is y = -2x+1.
Explanation.
Given:
The straight line passes throught the points (4,-3) and (2,1).
The objective is to find the equation of the line.
Consider the given points as,
[tex]\begin{gathered} (x_1,y_1)=(4,-3) \\ (x_2,y_2)=(2,1) \end{gathered}[/tex]The general equation of straight line is,
[tex]y=mx+b[/tex]Here, m stands for slope of the line and b stands for the yintercept of the line.
The slope of the line can be calculated by the formula,
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]Substitute the given values in the above formula.
[tex]\begin{gathered} m=\frac{1-(-3)}{2-4} \\ m=\frac{1+3}{-2} \\ m=\frac{4}{-2} \\ m=-2 \end{gathered}[/tex]Thus, the slope value is obtained.
Now, the value of b can be calculated by the equation,
[tex]y-y_1=m(x-x_1)[/tex]Substitute the obtained values in the above equation.
[tex]\begin{gathered} y-(-3)=-2(x-2) \\ y+3=-2(x-2) \\ y+3=-2x+4 \\ y=-2x+4-3 \\ y=-2x+1 \end{gathered}[/tex]By comparing the above equation with the equation of striaght line y = mx+b,
The value of b can be obtained as, b = +1.
Hence, the required final equation of the line is y = -2x+1.
