Question

Find the equation of the linethe line passes through the points (5,2) and (-4,-4)

Answer 1

`y = (2)/(3)x - (4)/(3)`

Explanation:

first find the slope using the above points then use the slope formula to calculate the slope

`m = (y2 - y1)/(x2 - x1) \\ (2 - - 4)/(5 - - 4) = (2 + 4)/(5 + 4) = (6)/(9) = (2)/(3)`

substitute ⅔ for m and one of the above points into the y-intercept form of the equation for a line and solve for b

`y = mx + b \\ 2 = (2)/(3) (5) + b \\ 2 = (10)/(3) + b \\ 2 - (10)/(3) = b \\ (6)/(3) - (10)/(3) = b \\ b = - (4)/(3)`

substitute the slope and the value for b into the equation to get the answer

`y = (2)/(3) x - (4)/(3)`