Question

Fill in the blanks.
(i) For the line 4x + 3y = 12, x-intercept = ...... and y-intercept = ......
(ii) If x = 4, y = 3 is a solution of 2x + ky = 14, then k = ......
(iii) If the point P(p, 4) lies on the line 3x + y = 10, then p = ......

Answer 1

(i) For the line 4x + 3y = 12, x-intercept = 3 and y-intercept= 4.

We will draw the graph of the number line by using the values of x and y axes given below.

x	0	3
y	4	0

So, the line intersects the x-axis at 3 and y-axis at 4.
(ii) If x = 4, y = 3 is a solution of 2x + ky = 14, then k = 2.

By putting the values of x and y we can find the value of .
$$\begin{gathered} 2x+ky=14 \\ \Rightarrow 2\left(4\right)+k\left(3\right)=14 \\ \Rightarrow 8+3k=14 \\ \Rightarrow 3k=14-8 \\ \Rightarrow 3k=6 \\ \Rightarrow k=2 \end{gathered}$$
(iii) If the point P(p, 4) lies on the line 3x + y = 10, then p = 2.

Since the point P(p,4) lies on the given line, it will satisfy the given equation of the line.
$$\begin{gathered} 3x+y=10 \\ \Rightarrow 3\left(p\right)+4=10 \\ \Rightarrow 3p=10-4 \\ \Rightarrow 3p=6 \\ \Rightarrow p=2 \end{gathered}$$