Respuesta :
y = 2x + 8 is the equation of line in slope intercept form
Solution:
Mike correctly found the slope and y-intercept of the line passing through the points (–5, –2) and (3, 14)
To find: Equation of the line in slope - intercept form
The equation of line in slope intercept form is:
y = mx + c ------ eqn 1
Where, "m" is the slope of line and "c" is the y intercept
Find the slope of line
[tex]m = \frac{y_2-y_1}{x_2-x_1}[/tex]
From given,
[tex](x_1, y_1) = (-5, -2)\\\\(x_2, y_2) = (3, 14)[/tex]
Therefore,
[tex]m = \frac{14-(-2)}{3-(-5)}\\\\m = \frac{14+2}{3+5}\\\\m = \frac{16}{8}\\\\m = 2[/tex]
Thus slope of line is 2
Find the y intercept:
Substitute m = 2 and (x, y) = (-5, -2) in eqn 1
-2 = 2(-5) + c
-2 = -10 + c
c = -2 + 10
c = 8
Thus the equation of line is:
Substitute c = 8 and m = 2 in eqn 1
y = 2x + 8
Thus the equation of line is found
