Question

The points (2, 5) and (6,-3) fall on a particular line. What is its equation in slope-intercept form?

y = -2
x+ ?

Answer 1

y = -2x + 9

Explanation:

slope intercept form : y = mx + b

where m = slope and b = y intercept

first let's find the slope

slope formula :

`m = ( (y2 - y1)/(x2 - x1) )`

where the x and y values are derived from the given points

here we are given (2,5) and (6,-3)

(x1,y1) = (2,5) so x1 = 2 and y1 = 5

(x2,y2) = (6,-3) so x2 = 6 and y2 = -3

we now plug these values into the formula

recall formula

`m= ( (y2 - y1)/(x2 - x1) )`

plug in x1 = 2, y1 = 5, x2 = 6 and y2 = -3

m = (-3 - 5) / ( 6 - 2 )

m = (-8)/(4)

m = -2

the slope is -2

now to find the y intercept we plug in the slope and the x and y value of a given point into slope intercept form and solve for b

y = mx + b

given point : (2,5) x = 2 , y = 5, m = -2

5 = -2(2) + b

5 = -4 + b

9 = b

so the equation would be y = -2x + 9