Question

graph the line with the equation $y = -\frac{2}{5}x + 1$.

Explanation:

Step1: Identify y-intercept

The equation is in slope-intercept form $y=mx+b$, where $b=1$. So the line crosses the y-axis at $(0, 1)$.

Step2: Use slope to find 2nd point

Slope $m=-\frac{2}{5}$, meaning $\frac{\text{change in } y}{\text{change in } x}=-\frac{2}{5}$. From $(0,1)$, move 5 units right and 2 units down to get $(5, 1-2)=(5, -1)$.

Step3: Plot and connect points

Mark $(0,1)$ and $(5,-1)$ on the grid, then draw a straight line through them. Extend the line to cover the graph.

Answer:

The line passes through points $(0, 1)$ and $(5, -1)$, and extends across the coordinate plane as shown by connecting these points and continuing along the slope $-\frac{2}{5}$.