Explanation:
no reason to panic. these are really easy principles :
the slope is always the ratio
y coordinate difference / x coordinate difference
when going from one point on the line to another.
so, e.g. when saying y changes by how many units, when x increments by one unit.
and the y-increment (representing the intersection point with the y-axis) is simply the y-value when x = 0 (that is when you intersect the y-axis).
regarding coordinates, they are just the x- and y-values of a point (particularly on a line).
so, to find an y-value to a given x-value, you pick the x-value on the x-axis and then go vertically straight up or down until you hit the curve or simple line. that "height" on the y-axis is the y-value.
and to find an x-value to a given y-value, you pick the y-value on the y-axis and then go horizontally straight right or left until you hit the curve or simple line. that side "offset" on the x-axis is the x-value.
so, the answer to the first question is
y = 0 (the line goes directly through (0, 0), when x = 0, so y = 0).
the slope (m) = -2
as when we increment x by 1, y changes by -2. so the slope ratio is -2/+1 = -2.
the answer to the second question is
the points for helicopter A are (4, 10), (8, 20).
the point for helicopter B is (6, 8).
remember, x stags for seconds (traveled), y for height in meters above the ground.
helicopter A is rising faster, because for every time period we pick, the height of helicopter A is higher than helicopter B, and in fact, the more seconds we pick as travel period, the higher away helicopter A gets.
we check this by a vertical line through the picked number of travel seconds and see where that vertical line intersects the travel lines of the 2 helicopters.
the answer to the third question is
a typical line equation is
y = mx + b
"m" being the slope, "b" being the y-intercept (see my explanations above).
b = -3 (y-value when x = 0)
m = the ratio when going from (0, -3) to (4, 0) :
x changes by +4 (from 0 to 4).
y changes by +3 (from -3 to 0).
the slope (m) is +3/+4 = 3/4
y = (3/4)x - 3
the answer to the fourth question is
y = -(1/2)x + 2
that means the slope is -1/2 (when x increases by 1, then y changes by -1/2, or when x increases by 2, then y changes by -1).
and the y-intercept is y = +2.
that makes it very simple for us. there is only one line that goes through (0, 2). and that is the first graph.
and yes, also the described slope fits there (but we don't even need this to decide, because the y-intercept makes it all clear as described).