Question

it is given that the x intercept and y intercept of a straight line L are 3 and 5 respectively. If L passes through P(k, 10) find the value of k.​

Answer 1

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:

$\displaystyle \frac{C}{3}x+\frac{C}{5}y=C$

Simplifying by C:

$\displaystyle \frac{x}{3}+\frac{y}{5}=1$

The point P(k,10) belongs to the line, thus:

$\displaystyle \frac{k}{3}+\frac{10}{5}=1$

Operating:

$\displaystyle \frac{k}{3}+2=1$

$\displaystyle \frac{k}{3}=-1$

Multiplying by 3:

$\boxed{k=-3}$