Step-by-step explanation:
the rate of change for lines is also called "slope" or "incline".
it is indicated by the factor of x in the equation.
in our case
y = x + 3 it is simply 1.
it residents the ratio of "y coordinate change / x coordinate change".
the bigger the number the steeper the line goes up (going from left to right on the grid).
so, we are looking for the answer options, where y change / x change > 1.
the first one is true.
I see the line goes through the points (-2, -3) and (1, 3).
so x changes +3 (from -2 to 1).
y changes by +6 (from -3 to +3)
and the slope is +6/+3 = 2.
the second one is true.
looking at the dues points
x changes by +6.
y changes by +9.
so, the slope is +9/+6 = 3/2 (also greater than 1).
the third one is false.
x changes by +5 (from-2 to +3).
y changes by +5 (from -7 to -2).
so, the slope is 1 and not greater than 1.
the fourth one is false.
I see e.g the points (0, 2) and (4, 4).
so, x changes by +4.
y changes by +2.
the slope is +2/+4 = 1/2 (and smaller than 1).
the fifth one is false.
x changes by +3.
y changes by +1.
so, the slope is +1/+3 = 1/3 (smaller than 1).
