Exercise 4.2

Given the point $(1, 2)$, find the equation of a line on which it lies. How many such lines are there?

Write the linear equation $\frac{x}{4}=1-\frac{y}{6}$ in the standard form. Draw its graph. From graph, find the points where it cuts the coordinate axes.

Draw the graph of the linear equation $x+y=7$. Verify from the graph that $\left(8, -1\right)$ is a solution of the given equation.

Draw the graph of the linear equation $2x+y=7$. Using graph, find the value of $x$ when the value of $y \text{is} 3$

Draw the graph of the linear equation $2x+y=7$. Using graph, find the value of $y$ when the value of $x \text{is} 4$. Also write one more solution of the given equation.

Draw the graph of the linear equation whose solutions are represented by the points having the sum of coordinates as $10 \text{units}$

Draw the graph of the linear equations $3x-2y=4$ and $x+y-3=0$ on the same graph paper and find the coordinates of the point of intersection of two lines.

Shade the triangular region formed by the graphs of the linear equations $2x+y=6$ and $2x-y+2=0$ and the $x-axis$. Write the coordinates of the vertices of the triangle and find its area.