Question

Find the \(x\) -intercept and the \(y\) -intercept of the line. Graph the equation. Label the points where the line crosses the axes. $$ 4 x+5 y=20 $$

Short answer

The \(x\)-intercept of the line is at (5,0) and the \(y\)-intercept is at (0,4). These are the points where the given line crosses the axes.

Step-by-step solution

Solving for \(x\)-intercept

To find the \(x\)-intercept, set \(y=0\) and solve for \(x\) in the given equation. The equation thus becomes \(4x + 5(0) = 20\), which simplifies to \(4x = 20\). By solving this equation we find that when \(y=0\), \(x=5\). Thus, the \(x\)-intercept of the line is at the point (5,0).

Solving for \(y\)-intercept

To find the \(y\)-intercept, set \(x=0\) and solve for \(y\) in the equation. The equation thus becomes \(4(0) + 5y = 20\), which simplifies to \(5y = 20\). Solving for \(y\) we find that when \(x=0\), \(y=4\). Thus, the \(y\)-intercept of the line is at the point (0,4).

Graphing the equation

To graph the equation, simply plot the intercept points from step 1 and 2 on a graph: that would be (0,4) and (5,0). Then draw a line that goes through these two points. Extend the line to the edges of the graph. The line represents all the solutions of the equation.