1) x-intercept: (15/4,0); y-intercept: (0,15/6)
2) Mother's present age: 30, Billy's age: 10, Jane's age: 2
Explanation:
1)
The equation of the line in this problem is
4x+6y−15=0
In order find the x-intercept, we replace y=0 into the equation and we find the value of x. We get:
And the y coordinate of this point is zero.
In order find the y-intercept, we replace x=0 into the equation and we find the value of y. We get:
And the x coordinate of this point is zero.
2)
To solve the problem, let's call:
b = age of Billy
j = age of Jane
m = age of the mother
Here we have:
- Billy is 5 times as old as Jane, so
b = 5j (1)
- The mother is 3 times as old as Billy, so
m = 3b (2)
- In 2 years from now, the mother will be 8 times as old as Jane, which means
m + 2 = 8 (j+2) (3)
where (j+2) is the age of Jane in 2 years from now.
Combining eq.(1) and (2) into (3), we get:
This is the age of Jane; so the age of the mother is:
And so, Billy's age is
Learn more about equations of lines:
brainly.com/question/3414323
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