A curve divides a plane into two areas, one satisfying the inequality (shaded) and one that does not (unshaded). So we can pick a point on either side (not on the curve itself) and substitute its x- and y-coordinates into the inequality. If the substituted values make the inequality true, then that point is in the shaded area. Otherwise, that point is in the unshaded area.
The answer to the problem is 29
Answer: a) y = - 3/2 x + 7/2
Step-by-step explanation:
The equation of a straight line can be represented in the slope-intercept form, y = mx + c
Where c = y intercept
m represents the slope of the line.
m = (y2 - y1)/(x2 - x1)
y2 = final value of y
y 1 = initial value of y
x2 = final value of x
x1 = initial value of x
The line passes through (3, - 1) and (- 1, 5),
y2 = 5
y1 = -1
x2 = - 1
x1 = 3
Slope,m = (5 - - 1)/(- 1 - 3) = 6/- 4 =
- 3/2
To determine the y intercept, we would substitute x = 3, y = - 1 and m= - 3/2 into y = mx + c. It becomes
- 1 = - 3/2 × 3 + c
- 1 = - 9/2 + c
c = - 1 + 9/2
c = 7/2
The equation becomes
y = - 3x/2 + 7/2
