Question

Find the \(x\) -intercept and the \(y\) -intercept of the line. Graph the equation. Label the points where the line crosses the axes. $$ 0.5 y=-2 x+8 $$

Short answer

The x-intercept is 4 and the y-intercept is 16. These points are plotted on the graph and a line passing through them is drawn.

Step-by-step solution

Finding the x-intercept

To find the x-intercept, set \(y = 0\) in the given equation, \(0.5 y = -2x +8\). This gives \(0 = -2x +8\). Solving this for \(x\) will give us the x-intercept.

Finding the y-intercept

To find the y-intercept, set \(x = 0\) in the given equation, \(0.5 y = -2x + 8\). This gives \(0.5 y = 8\). Solving this for \(y\) will give us the y-intercept.

Graphing and labelling

Now, plot these intercepts in a graph and draw a line passing through the intercepts. Finally, label the x-intercept and y-intercept on the graph.