Respuesta :
[tex]y = \frac{-8}{3}x + 10[/tex] is the equation in slope intercept form
Solution:
Given points are (0, 10) and (3, 2)
We have to find the slope intercept form
Let us first find the slope of line
The slope of line is given as:
[tex]m = \frac{y_2-y_1}{x_2-x_1}[/tex]
Here,
[tex](x_1, y_1) = (0, 10)\\\\(x_2, y_2) =(3,2)[/tex]
Substituting the values we get,
[tex]m = \frac{2-10}{3-0}\\\\m = \frac{-8}{3}[/tex]
The equation of line in slope intercept form is given as:
y = mx + c ------- eqn 1
Where, "m" is the slope of line and "c" is the y intercept
Substitute [tex]m = \frac{-8}{3}[/tex] and (x , y) = (0, 10) in eqn 1
[tex]10 = \frac{-8}{3} \times 0 + c\\\\c = 10[/tex]
[tex]Substitute\ m = \frac{-8}{3}\ and\ c = 10\ in\ eqn\ 1[/tex]
[tex]y= \frac{-8}{3}x + 10[/tex]
Thus the equation of line in slope intercept form is found
