Graph the Linear Equation $-y + \frac{3}{5}x = 0$ (Slope-Intercept Form)

Question

Graph the linear equation $-y + \frac{3}{5}x = 0$.

Accepted Answer

The graph is a straight line passing through the origin (0, 0) with a slope of $\frac{3}{5}$ (e.g., passing through (5, 3) and (-5, -3)).

Answer

Step 1: Rearrange the equation to slope-intercept form ($y = mx + b$): \nStart with $-y + \frac{3}{5}x = 0$. Add $y$ to both sides: $\frac{3}{5}x = y$, so $y = \frac{3}{5}x$. Step 2: Identify the y-intercept ($b$) and slope ($m$): \n- The y-intercept $b = 0$, so the line passes through $(0, 0)$. \n- The slope $m = \frac{3}{5}$ (rise = 3, run = 5). Step 3: Plot a second point using the slope: \nFrom $(0, 0)$, move 5 units right (run) and 3 units up (rise) to $(5, 3)$. (Alternatively, move 5 units left and 3 units down to $(-5, -3)$.) Step 4: Draw a straight line through the points $(0, 0)$ and $(5, 3)$ (or $(-5, -3)$).