Question

1) Point W(-2,y) is a point on a line with a slope of -2 that also passes through E(3,-5). Find the coordinates of W?

2) Point A(6,0) is a point on a line with a slope of -1/2 that also passes through H(x,3). Find y. Find the coordinates of H?

Answer 1

For 1), we know that the slope is 2, so in y=mx+b (an equation to represent a straight line), m=-2. x and y remain the same, so we just have to find b. In y=-2x+b, we know that it passes through point E, so we can plug that in and see what b has to equal. Doing just that, we get -5=-2(3)+b=-6+b. Adding 6 to both sides using the addition property of equality, to separate the b we get 1=b, making the equation y=-2x+1. Plugging -2 in for x (as that's the x value of point W), we get -2(-2)+1=y=4+1=5, making the point (-2, 5)

For 2), we use a similar strategy - y=(-1/2)x+b, plug it in for point A to get 0=(-1/2)*6+b=-3+b. Adding 3 to both sides to separate the b , we get 3=b to make our equation y=(-1/2)x+3. Plugging that into H, where y=3, we get 3=(-1/2)x+3. Subtract 3 from both sides to get 0=(-1/2)x, and multiply both sides by 2 to separate the x and get 0=x, making H=(0, 3)

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