A line passes through the points (-4,-9) and (-2,-6). What is the equation of the line in Slope-Intercept Form?

y = (3/2)x - 3

Step-by-step explanation:

given:

coordinates :

(-4, -9) (-4 = x1, -9 = y1)

and

(-2, -6) (-2 = x2, -6 = y2)

slope (m) = rise / run = (y2-y1) / (x2-x1)

=> -6- (-9) / -2 - (-4)

=> -6+9 / -2 + 4

=> 3 / 2

=> y= mx + b

=> y = (3/2)x + b

To find (b) or the y-intercept:

=> y = (3/2)x + b

=> y - (3/2)x = b

case 1

=>when x = -2 and y = -6,

=> -6 - (3/2) × -2 = b

=> -6 + 6/2 = b

=> -6 + 3 = b

=> -3 = b

case 2

=> when x = -4 and y = -9,

=> -9 - (3/2) × -4 = b

=> -9 + 12/2 = b

=> -9 + 6 = b

=> -3 = b

so, as we can see, in both the cases of taking different pair of coordinates, we are getting the same value of (b) or the y-intercept.

now,

b = -3

m = (3/2)

therefore,

y = (3/2)x - 3

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answer: it is d

step-by-step explanation: