Use intercepts to graph each equation. 6x-3y+15=0

Verified step by step guidance

1. Rewrite the equation in standard form to make it easier to find the intercepts: $6x\; -\; 3y\; +\; 15\; =\; 0$.
2. To find the x-intercept, set $y\; =\; 0$ in the equation and solve for $x$. Substitute $y\; =\; 0$ into $6x\; -\; 3y\; +\; 15\; =\; 0$, which simplifies to $6x\; +\; 15\; =\; 0$. Solve for $x$.
3. To find the y-intercept, set $x\; =\; 0$ in the equation and solve for $y$. Substitute $x\; =\; 0$ into $6x\; -\; 3y\; +\; 15\; =\; 0$, which simplifies to $-3y\; +\; 15\; =\; 0$. Solve for $y$.
4. Plot the x-intercept and y-intercept on the 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 to graph the equation. This line represents the solution to the equation $6x\; -\; 3y\; +\; 15\; =\; 0$.

Key Concepts

Intercepts

Intercepts are points where a graph intersects the axes. The x-intercept occurs when y=0, and the y-intercept occurs when x=0. For the equation 6x - 3y + 15 = 0, finding these intercepts helps in plotting the graph accurately.

Linear Equations

A linear equation represents a straight line when graphed on a coordinate plane. The general form is Ax + By + C = 0, where A, B, and C are constants. The equation given can be rearranged to slope-intercept form (y = mx + b) to identify the slope and y-intercept.

Graphing Techniques

Graphing techniques involve methods to visually represent equations on a coordinate plane. For linear equations, plotting the intercepts and using the slope to find additional points allows for an accurate representation of the line. Understanding these techniques is essential for effective graphing.