Question

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

Answer 1

Answer:

$y = - \frac{5}{4} x - \frac{1}{2}$

Step-by-step explanation:

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

$\boxed{ slope = \frac{y _{1} - y_2 }{x_1 - x_2} }$

Slope

$= \frac{ - 3 - \frac{1}{8} }{2 - ( - \frac{1}{2}) }$

$= - \frac{5}{4}$

Substitute the value of m into the equation:

$y = - \frac{5}{4} x + c$

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

When x= 2, y= -3,

$- 3 = - \frac{5}{4} (2) + c$

$- 3 = - \frac{5}{2} + c$

$c = - 3 + \frac{5}{2}$

$c = - \frac{1}{2}$

Thus, the equation of the line is $y = - \frac{5}{4} x - \frac{1}{2}$.