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:
[tex]4x+6(0)-15=0[/tex]
[tex]4x-15=0[/tex]
[tex]x=\frac{15}{4}[/tex]
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:
[tex]4(0)+6y-15=0[/tex]
[tex]6y-15=0[/tex]
[tex]y=\frac{15}{6}[/tex]
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:
[tex]m = 3(5j) = 15j[/tex]
[tex]15j +2 = 8j+16[/tex]
[tex]7j=14[/tex]
[tex]j=\frac{14}{7}=2[/tex]
This is the age of Jane; so the age of the mother is:
[tex]m=15j=15(2)=30[/tex]
And so, Billy's age is
[tex]b=\frac{m}{3}=10[/tex]
Learn more about equations of lines:
brainly.com/question/3414323
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