Questions: Write an equation of the line passing through point P(0,1) that is parallel to the line y=-2x+3. An equation is:

Transcript text: Write an equation of the line passing through point $P(0,1)$ that is parallel to the line $y=-2 x+3$. An equation is: $\square$

Solution

Solution Steps

Step 1: Identify the slope of the given line

The given line is $ y = -2x + 3 $. The slope of this line is $-2$.

Step 2: Use the point-slope form to find the equation of the parallel line

The line passing through point $ P(0,1) $ and parallel to $ y = -2x + 3 $ will have the same slope, $-2$. Using the point-slope form $ y - y_1 = m(x - x_1) $, where $ m $ is the slope and $ (x_1, y_1) $ is the point, we get: \[ y - 1 = -2(x - 0) \] \[ y - 1 = -2x \] \[ y = -2x + 1 \]

Final Answer

The equation of the line passing through point $ P(0,1) $ that is parallel to the line $ y = -2x + 3 $ is: \[ y = -2x + 1 \]

{"axisType": 3, "coordSystem": {"xmin": -5, "xmax": 5, "ymin": -5, "ymax": 5}, "commands": ["y = -2x + 3", "y = -2x + 1"], "latex_expressions": ["$y = -2x + 3$", "$y = -2x + 1$"]}

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