Question

graph this line using the slope and y - intercept: y = -\frac{1}{3}x + 5 click to select points on the graph.

Explanation:

Step1: Identify y - intercept

The equation is in slope - intercept form $y = mx + b$, where $b$ is the y - intercept. For $y=-\frac{1}{3}x + 5$, $b = 5$. So, plot the point $(0,5)$ on the graph.

Step2: Identify slope

The slope $m=-\frac{1}{3}$. This means for every 3 units we move to the right along the x - axis, we move 1 unit down along the y - axis. Starting from the point $(0,5)$, if we move 3 units to the right (x = 3), then $y=-\frac{1}{3}(3)+5=- 1 + 5=4$. So, we can plot the point $(3,4)$. We can also move in the opposite direction. For every 3 units we move to the left along the x - axis, we move 1 unit up along the y - axis. Starting from $(0,5)$, if we move 3 units to the left (x=-3), then $y=-\frac{1}{3}(-3)+5 = 1 + 5=6$. So, we can plot the point $(-3,6)$. Then draw a straight line through these points.

Answer:

Plot the points $(0,5)$, $(3,4)$, $(-3,6)$ and draw a straight line through them.