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

Answer:

$y = \frac{3}{2} x + 2$

Step-by-step explanation:

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

$\boxed{slope = \frac{y1 - y2}{x1 - x2} }$

Using the formula above,

$slope = \frac{5 - ( - 4)}{2 - ( - 4)}$

$m = \frac{5 + 4}{2 + 4}$

$m = \frac{9}{6}$

$m = \frac{3}{2}$

Substitute the value of m into the equation:

$y = \frac{3}{2} x + b$

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

When x= 2, y= 5,

$5 = \frac{3}{2} (2) + b$

5= 3 +b

b= 5 -3

b= 2

Thus, the equation of the line is $y = \frac{3}{2} x + 2$.