Step-by-step explanation:
a typical line function (slope-intercept form) is
y = ax + b
a is the slope of the function (the ratio of " y coordinate change / x coordinate change"), and b is the y-intercept (the y value when x = 0).
1.
y = -3x - 7
2.
we see that when x changes e.g. by +3 units, y changes by -2 units.
so, the slope is -2/3.
3.
when x = 0, the y value = -3.
that is as explained the y-intercept.
4.
we see the y-intercept right with the first point, as x = 0 there. so, the y-intercept is the y value there = 5.
and the slope we see when going from one point to the other :
x changes by +3 units (from 0 to 3).
y changes by -1 unit (from 5 to 4).
so, the slope is -1/3
and the equation is :
y = -1/3 × x + 5 = -x/3 + 5
5.6.7.
we just need to use the x values in the equation and calculate the resulting y values :
for x = -1
y = 2×-1 + 3 = -2 + 3 = 1
for x = 0
y = 2×0 + 3 = 0 + 3 = 3
for x = 1
y = 2×1 + 3 = 2 + 3 = 5
