Answer:
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
