Determine the equation of a line passing through the point A(6;4) B(2;0)

Question

ScanSolve AI Tutor · Accepted Answer

Let's determine the equation of the line passing through the points A(6, 4) and B(2, 0).

Calculate the slope ( $m$ ) of the line.
The formula for the slope is $m = \frac{y_2 - y_1}{x_2 - x_1}$ .
Let $(x_1, y_1) = (6, 4)$ and $(x_2, y_2) = (2, 0)$ .
$m = \frac{0 - 4}{2 - 6}$ $m = \frac{-4}{-4}$ $m = 1$
Use the slope-intercept form of a linear equation, $y = mx + c$ .
Substitute the calculated slope $m=1$ into the equation:
$y = 1x + c$ $y = x + c$
Substitute one of the given points into the equation to find the y-intercept ( $c$ ).
Let's use point B(2, 0):
$0 = 2 + c$ $c = 0 - 2$ $c = -2$
Write the final equation of the line using the slope and y-intercept.
$y = x - 2$

Answer