Questions: Use the starting point and slope to graph the following equation: y=8/6 x+1

Transcript text: Use the starting point and slope to graph the following equation: \[ y=\frac{8}{6} x+1 \]

Solution

Solution Steps

Step 1: Identify the Slope and Y-Intercept

The given equation is $ y = \frac{8}{6}x + 1 $. This is in the slope-intercept form $ y = mx + b $, where $ m $ is the slope and $ b $ is the y-intercept.

Slope ($ m $): $ \frac{8}{6} = \frac{4}{3} $
Y-intercept ($ b $): 1

Step 2: Determine the Starting Point

The starting point is the y-intercept, which is the point where the line crosses the y-axis. This point is $ (0, 1) $.

Step 3: Use the Slope to Find Another Point

From the starting point $ (0, 1) $, use the slope $ \frac{4}{3} $ to find another point on the line. The slope indicates that for every 3 units moved to the right (positive x-direction), the line moves up 4 units (positive y-direction).

Starting from $ (0, 1) $, move 3 units to the right to $ (3, 1) $.
Then move up 4 units to $ (3, 5) $.

Final Answer

The line passes through the points $ (0, 1) $ and $ (3, 5) $ with a slope of $ \frac{4}{3} $.

{"axisType": 3, "coordSystem": {"xmin": -5, "xmax": 5, "ymin": -5, "ymax": 5}, "commands": ["y = (4/3)x + 1"], "latex_expressions": ["$y = \\frac{8}{6}x + 1$"]}

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