Step-by-step explanation:
the slope is actually a ratio y/x indicating how many units y changes, when x changes a certain amount of units when going from one point to another.
so, any line parallel to another line must have the same slope.
the slope of a perpendicular line (crosses the other line in a 90 degree angle) simply changes x and y upside-down and flips the sign (+ to -, or - to +).
the y-intercept is the y value when x = 0. so, it is b in the equation.
1a.
parallel, so it has the same slope. and the point is (0, 4), so x=0 there. therefore, the y value 4 is the y-intercept.
y = (2/5)x + 4
1b.
remember the description above about the slope of perpendicular lines. and the y-intercept follows the same principle as for any other line.
y = (-5/2)x + 4
2a.
everything is already there.
the perpendicular slope is -6/1 = -6
y - 4 = -6×(x - -1) = -6×(x + 1)
3a.
we need to read the coordinates and therefore the slope in the graph.
it seems F = (0, 2) and G = (2, 1)
for the slope, x changes by +2 (from 0 to 2), y changes by -1 (from 2 to 1).
the slope is
-1/2
a line parallel to this line has the same slope.
so,
y - 5 = (-1/2)×(x - 3)
