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The x-intercept of a line is where the line crosses the x-axis. This point has a y-coordinate of zero. To find the x-intercept from a linear equation, set \( y = 0 \) and solve for the variable \( x \). For the equation \( 2x - y = 7 \), you substitute \( y = 0 \) to get \( 2x = 7 \). Solving for \( x \) gives you \( x = \frac{7}{2} \), so the x-intercept is (3.5, 0).

Finding an x-intercept is crucial because it gives you an exact point on the graph. This helps to confirm that your graph is accurate.

Things to remember:

• Set \( y = 0 \) in the equation.
• Solve for \( x \) to find the x-intercept.
• The x-intercept is always written as \( (x, 0) \).

The y-intercept is the point where the line intersects the y-axis. At this point, the x-coordinate is zero. To find the y-intercept, set \( x = 0 \) in the linear equation and then solve for \( y \).

For the given equation \( 2x - y = 7 \), by setting \( x = 0 \), the equation becomes \( -y = 7 \). Solving gives you \( y = -7 \). Thus, the y-intercept is \( (0, -7) \).

The y-intercept is especially useful, as it's another precise point that ensures your line is correctly drawn on the graph.

Some tips for finding the y-intercept:

• Set \( x = 0 \) in the equation.
• Solve for \( y \) to determine the y-intercept.
• The y-intercept is presented as \( (0, y) \).

Graphing linear equations using algebraic techniques involves plotting points determined by solving the equation and using these points to draw the line. Two critical points in this process are the x-intercept and y-intercept. However, using a checkpoint, as part of algebraic graphing, helps in ensuring that the line is drawn correctly and represents the equation accurately.

After finding the intercepts, choose another x value (other than the x-intercept), plug it into the equation, and solve for y to get a checkpoint. For example, with \( x = 2 \) in \( 2x - y = 7 \), you find \( y = -1 \), obtaining the checkpoint \( (2, -1) \).

Steps for algebraic graphing techniques:

• Identify and plot the x-intercept on the graph.
• Determine and plot the y-intercept.
• Find another point by choosing a random x value as a checkpoint.
• Draw a line through these points to graph the equation accurately.

Using these algebraic techniques simplifies the graphing process and ensures accuracy, providing a visual representation of the equation.