Question

Write the equation of a line in slope-intercept form, y = mx + b, between the following

points: (2, 5) and (-4,-4).

Answer 1

`y = (3)/(2) x + 2`

Explanation:

In the slope-intercept form y= mx +b, m is the slope and b is the y- intercept.

`\boxed{slope = (y1 - y2)/(x1 - x2) }`

Using the formula above,

`slope = (5 - ( - 4))/(2 - ( - 4))`

`m = (5 + 4)/(2 + 4)`

`m = (9)/(6)`

`m = (3)/(2)`

Substitute the value of m into the equation:

`y = (3)/(2) x + b`

To find the value of b, substitute a pair of coordinates into the equation.

When x= 2, y= 5,

`5 = (3)/(2) (2) + b`

5= 3 +b

b= 5 -3

b= 2

Thus, the equation of the line is
`y = (3)/(2) x + 2`.