Graph using intercepts: 2x - 5y - 10 = 0

Verified step by step guidance

1. Rewrite the equation in standard form if necessary. The given equation is already in standard form: $2x\; -\; 5y\; -\; 10\; =\; 0$.
2. To find the x-intercept, set $y\; =\; 0$ in the equation and solve for $x$. Substitute $y\; =\; 0$ into $2x\; -\; 5y\; -\; 10\; =\; 0$, which simplifies to $2x\; -\; 10\; =\; 0$. Solve for $x$.
3. To find the y-intercept, set $x\; =\; 0$ in the equation and solve for $y$. Substitute $x\; =\; 0$ into $2x\; -\; 5y\; -\; 10\; =\; 0$, which simplifies to $-5y\; -\; 10\; =\; 0$. Solve for $y$.
4. Plot the x-intercept and y-intercept on a coordinate plane. The x-intercept is the point where the graph crosses the x-axis, and the y-intercept is the point where the graph crosses the y-axis.
5. Draw a straight line through the two intercepts. This line represents the graph of the equation $2x\; -\; 5y\; -\; 10\; =\; 0$.

Key Concepts

Intercepts

Intercepts are points where a graph crosses the axes. The x-intercept occurs when y = 0, and the y-intercept occurs when x = 0. Finding these points is essential for graphing linear equations, as they provide two key coordinates that define the line's position on the Cartesian plane.

Linear Equations

A linear equation is an equation of the first degree, meaning it can be expressed in the form Ax + By + C = 0, where A, B, and C are constants. The graph of a linear equation is a straight line, and understanding its structure helps in identifying its slope and intercepts, which are crucial for graphing.

Slope-Intercept Form

The slope-intercept form of a linear equation is given by y = mx + b, where m represents the slope and b represents the y-intercept. While the question focuses on intercepts, converting the equation to this form can provide additional insights into the line's steepness and direction, enhancing the graphing process.