Question

Write the equation in slope-intercept form. Then graph the equation. $$5 x+3 y=3$$

Short answer

The slope-intercept form of the equation is \(y = -\frac{5}{3}x + 1\). The graph of the equation would begin at the y-intercept (0,1) and slope downward to the right.

Step-by-step solution

Convert to Slope-Intercept Form

The equation should first be rewritten as \(3y = -5x + 3\), by subtracting \(5x\) from both sides.

Isolate y

Then, isolate \(y\), by dividing the entire equation by 3. This will yield \(y = -\frac{5}{3}x + 1\).

Identify the Slope and Y-intercept

Now that the equation is in slope-intercept form, the slope (\(m\)) can be identified as \(-\frac{5}{3}\) and the y-intercept (\(c\)) as 1.

Graph the Equation

First, plot the y-intercept (0,1) on the graph. The slope means that for each 3 units move to the right along the x-axis, move down 5 units. Continue this until several points are plotted. Then, connect these points to form the line representing the equation.