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

k=-3

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 (C)/(3)x+(C)/(5)y=C`

Simplifying by C:

`\displaystyle (x)/(3)+(y)/(5)=1`

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

`\displaystyle (k)/(3)+(10)/(5)=1`

Operating:

`\displaystyle (k)/(3)+2=1`

`\displaystyle (k)/(3)=-1`

Multiplying by 3:

`\boxed{k=-3}`