Question

What is the equation of the line that passes through (4,3) and (2, -1)?A. y = 2x-5B. y = 4x -13C. y = 6x+4D. y = 1/2 x -2

Answer 1

y = 2x -5. Option A is correct

Explanations:

The equation of a line in slope-intercept form is expressed as:

`y=mx+b`

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:

`\begin{gathered} slope=(y_2-y_1)/(x_2-x_1) \\ slope=(-1-3)/(2-4) \\ slope=(-4)/(-2) \\ slope=2 \end{gathered}`

Determine the y-intercept" "b"

Using the coordinate point (4, 3) and m = 2

`\begin{gathered} y=mx+b \\ 3=2(4)+b \\ 3=8+b \\ b=3-8=-5 \end{gathered}`

Determine the required equation

`\begin{gathered} y=mx+b \\ y=2x+(-5) \\ y=2x-5 \end{gathered}`

Hence the equation of the line that passes through (4,3) and (2, -1) is y = 2x -5