Question

Write an equation in slope-intercept form of the line that passes through (2,-3) and (- 1/2, 1/8)​

Answer 1

`y = - (5)/(4) x - (1)/(2)`

Explanation:

Slope-intercept form: y= mx +c, where m is the slope and c is the y-intercept.

`\boxed{ slope = (y _(1) - y_2 )/(x_1 - x_2) }`

Slope

`= ( - 3 - (1)/(8) )/(2 - ( - (1)/(2)) )`

`= - (5)/(4)`

Substitute the value of m into the equation:

`y = - (5)/(4) x + c`

To find the value of c, substitute a pair of coordinates the line passes through into the equation.

When x= 2, y= -3,

`- 3 = - (5)/(4) (2) + c`

`- 3 = - (5)/(2) + c`

`c = - 3 + (5)/(2)`

`c = - (1)/(2)`

Thus, the equation of the line is
`y = - (5)/(4) x - (1)/(2)`.