Question

Find the \(x\) -intercept and the \(y\) -intercept of the line. Graph the equation. Label the points where the line crosses the axes. $$ 2 x+4 y=16 $$

Short answer

The x-intercept is 8 and the y-intercept is 4

Step-by-step solution

Determine the x-intercept

The x-intercept is the value of x when y=0. We start by setting \(y = 0\) in the equation \(2x + 4y = 16\). After substituting \(y=0\) to the equation, we get \(2x = 16\). Then, solve for \(x\) by dividing by 2.

Determine the y-intercept

The y-intercept is the value of \(y\) when \(x=0\). We start by setting \(x = 0\) in the equation \(2x + 4y = 16\). After substituting \(x=0\) to the equation, we get \(4y = 16\). Then, solve for \(y\) by dividing by 4.

Plot the x and y intercepts

Plot the points where the line crosses the axes i.e., (x-intercept,0) and (0,y-intercept) on the graph, and link those two points with a straight line to represent the line for the given equation.