The equation of the line given is $4x - 2y = 14$. Let's find the x-intercept and y-intercept step by step.

1. Find the x-intercept:

To find the x-intercept, set $y = 0$ in the equation and solve for $x$: $4x - 2(0) = 14 \quad \Rightarrow \quad 4x = 14 \quad \Rightarrow \quad x = \frac{14}{4} = 3.5$ So, the x-intercept is $x = 3.5$.

2. Find the y-intercept:

To find the y-intercept, set $x = 0$ in the equation and solve for $y$: $4(0) - 2y = 14 \quad \Rightarrow \quad -2y = 14 \quad \Rightarrow \quad y = \frac{14}{-2} = -7$ So, the y-intercept is $y = -7$.

Summary:

• x-intercept: $x = 3.5$ or $(3.5, 0)$
• y-intercept: $y = -7$ or $(0, -7)$

Plotting the Line:

• Plot the point $(3.5, 0)$ on the x-axis.
• Plot the point $(0, -7)$ on the y-axis.
• Draw a straight line through these two points to represent the graph of the line.

Would you like to proceed with the graphical representation or need more details?

Here are some related questions for further understanding:

1. How do you find the slope of a line given two points?
2. How can you convert the equation $4x - 2y = 14$ to slope-intercept form?
3. What does the slope represent in the context of a linear equation?
4. How can you verify that a point lies on a line?
5. How do you determine the distance between two points on a graph?

Tip: To quickly find the intercepts of a linear equation, remember that the x-intercept occurs when $y = 0$ and the y-intercept occurs when $x = 0$.