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We need to find the equation for the boundary line. It goes through the two points (1,-1) and (2,-5)
Find the slope of the line through (x1,y1) = (1,-1) and (x2,y2) = (2,-5)
m = (y2 - y1)/(x2 - x1)
m = (-5 - (-1))/(2 - 1)
m = (-5 + 1)/(2 - 1)
m = -4/1
m = -4 is the slope
Plug m = -4 and (x1,y1) = (1,-1) into the point slope formula. Solve for y.
y - y1 = m(x - x1)
y - (-1) = -4(x - 1)
y + 1 = -4(x - 1)
y + 1 = -4x + 4 ... distributing
y + 1 - 1 = -4x + 4 - 1 ... subtracting 1 from both sides
y = -4x + 3 is the equation of the boundary line
The blue shaded region tells us to consider all points below this boundary line as solutions. So we will use a "less than" sign to indicate this
We go from y = -4x+3 to y < -4x+3 which is the answer we want.
We do not have a line under the inequality sign. Simply because the boundary is a dashed line, so we exclude points on the boundary line as solutions. If we had , then the boundary line would be solid and it would tell the reader "points on the boundary line are part of the solution set".
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I like point point form because it doesn't fail in the no slope case. The line through (a,b) and (c,d) is
(c-a)(y-b) = (d-b)(x-a)
Point slope form is almost the same,
1. (a,b)=(4,0),(c,d)=(-2,1)
y - 0 = (1 - 0)/(-2 - 4) (x - 4)
Answer: y = (-1/6)(x-4)
2.
y - -2 = (3 - -2)/(5 - -3) (x - -3)
Answer: y + 2 = (5/8) (x+3)
3.
y - 1 = (4 - 1)/(3 - -5) (x - -5)
Answer: y - 1 = (3/8) (x+5)
Answer:
Step-by-step explanation:
Product of of 3 and b is 3b
At least means greater than or equal too.
