y = 2x -5. Option A is correct
The equation of a line in slope-intercept form is expressed as:
[tex]y=mx+b[/tex]where:
m is the slope
b is the intercept
The slope of the line passing through the coordinates (4,3) and (2, -1) is given as:
[tex]\begin{gathered} slope=\frac{y_2-y_1}{x_2-x_1} \\ slope=\frac{-1-3}{2-4} \\ slope=\frac{-4}{-2} \\ slope=2 \end{gathered}[/tex]Determine the y-intercept" "b"
Using the coordinate point (4, 3) and m = 2
[tex]\begin{gathered} y=mx+b \\ 3=2(4)+b \\ 3=8+b \\ b=3-8=-5 \end{gathered}[/tex]Determine the required equation
[tex]\begin{gathered} y=mx+b \\ y=2x+(-5) \\ y=2x-5 \end{gathered}[/tex]Hence the equation of the line that passes through (4,3) and (2, -1) is y = 2x -5
