Let’s solve the problem step-by-step:

(a) Draw a ring around the equation of the line.

The line on the grid has a slope of 2, and it passes through the point $(0, -2)$ (the $y$-intercept). This matches the equation $y = 2x - 2$.

The correct answer is: $y = 2x - 2$

(b) A different equation is $2x + y = 4$. Complete the table of values.

We rearrange the equation $2x + y = 4$ to express $y$ in terms of $x$: $y = 4 - 2x$

Now substitute the given $x$-values into the equation $y = 4 - 2x$:

1. When $x = 0$:
   $y = 4 - 2(0) = 4$

2. When $x = 3$:
   $y = 4 - 2(3) = -2$

The completed table is:

(c) Draw the line $2x + y = 4$ on the same grid.

Using the table of values:

1. Plot the point $(0, 4)$.
2. Plot the point $(3, -2)$.
3. Draw a straight line passing through these points.

Would you like me to explain how to plot the line in more detail or analyze further? 😊

5 Related Questions:

1. How do you determine the slope of a line from its equation?
2. What is the difference between slope-intercept form ($y = mx + b$) and standard form ($Ax + By = C$) of a linear equation?
3. How can you check if a point lies on a given line?
4. What is the significance of the $y$-intercept in a linear equation?
5. How do you convert between standard form and slope-intercept form of a line?

Tip:

To verify your plotted line, substitute the coordinates of your points into the original equation and ensure the equation holds true!