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Question

1. What are the y and x-intercepts of -(1/2)x - (2/3)y = 3/4?

2. What are the y and x-intercepts of -0.3x - 0.5y = 0.15?

Thanks very much for helping.

Answer 1

1. To find the x-intercept, set y = 0 and solve for x:

-(1/2)x - (2/3)y = 3/4
-(1/2)x - (2/3)(0) = 3/4
-(1/2)x = 3/4
x = (3/2)4
x = 6

To find the y-intercept, set x = 0 and solve for y:

-(1/2)x - (2/3)y = 3/4
-(1/2)(0) - (2/3)y = 3/4
-(2/3)y = 3/4
y = (3/2)3
y = 9/2

2. To find the x-intercept, set y = 0 and solve for x:

-0.3x - 0.5y = 0.15
-0.3x - 0.5(0) = 0.15
-0.3x = 0.15
x = 0.15/0.3
x = 0.5

To find the y-intercept, set x = 0 and solve for y:

-0.3x - 0.5y = 0.15
-0.3(0) - 0.5y = 0.15
-0.5y = 0.15
y = 0.15/0.5
y = 0.3

Answer 2

-(1/2)x - (2/3)y = 3/4
multiply both sides by 4/3 to get
-2/3 x - 8/9 y = 1
so the intercepts are (-3/2,0) and (0,-9/8)

-0.3x - 0.5y = 0.15
-2x - 10/3 y = 1
the intercepts are (-1/2,0) and (0,-3/10)