Question

Mike correctly found the slope and y-intercept of the line passing through the points (–5, –2) and (3, 14) as follows. m = StartFraction 14 minus (negative 2) Over 3 minus (negative 5) EndFraction = StartFraction 16 Over 8 EndFraction = 2. y = 2 x + b. Negative 2 = 2 (negative 5) + b. Negative 2 + 10 = negative 10 + b + 10. b = 8. What is the equation of the line in slope-intercept form?

Answer 1

the answer is y=2x+8

Explanation:

Answer 2

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

`m = (y_2-y_1)/(x_2-x_1)`

From given,

`(x_1, y_1) = (-5, -2)\\\\(x_2, y_2) = (3, 14)`

Therefore,

`m = (14-(-2))/(3-(-5))\\\\m = (14+2)/(3+5)\\\\m = (16)/(8)\\\\m = 2`

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