Question

Find the \(x\) -intercept and the \(y\) -intercept of the line. Graph the equation. Label the points where the line crosses the axes. $$ y=4 x+8 $$

Short answer

The x-intercept is -2 and the y-intercept is 8. The line intersects the axes at these points.

Step-by-step solution

Find the x-intercept

Set \(y = 0\) in the given equation and solve for \(x\):\n\n0 = 4x + 8\n\nThis simplifies to \(x = -2\). So, the x-intercept is -2.

Find the y-intercept

Set \(x = 0\) in the given equation and solve for \(y\):\n\ny = 4(0) + 8\n\nThis simplifies to \(y = 8\). So, the y-intercept is 8.

Graph the equation

Now graph the line using the x and y intercepts. The line will cross the x-axis at \(x = -2\) and the y-axis at \(y = 8\). Label these points on the graph.