Answer:
k=-3
Step-by-step explanation:
Equation of a line
The general equation of a line can be written as:
Ax+By=C
The x-intercept is the point where the line crosses the x-axis, i.e. y=0, thus replacing x=3 and y=0:
A(3)+B(0)=C
3A=C
Solving for A:
A=C/3
The y-intercept is the point where the line crosses the y-axis, i.e. x=0, thus replacing x=0 and y=5:
A(0)+B(5)=C
5B=C
Solving for B:
B=C/5
Replacing into the general equation:
[tex]\displaystyle \frac{C}{3}x+\frac{C}{5}y=C[/tex]
Simplifying by C:
[tex]\displaystyle \frac{x}{3}+\frac{y}{5}=1[/tex]
The point P(k,10) belongs to the line, thus:
[tex]\displaystyle \frac{k}{3}+\frac{10}{5}=1[/tex]
Operating:
[tex]\displaystyle \frac{k}{3}+2=1[/tex]
[tex]\displaystyle \frac{k}{3}=-1[/tex]
Multiplying by 3:
[tex]\boxed{k=-3}[/tex]