Sovi AI

Pregunta

Pasos de solución

1. Understand the question

   trazar la recta.
   $y = -\\frac{3}{2}x - 3$

2. Explanation

   Step1: Identify the y - intercept

   The equation of the line is in slope - intercept form \(y = mx + b\), where \(m\) is the slope and \(b\) is the y - intercept. For the equation \(y=-\frac{3}{2}x - 3\), the y - intercept \(b=- 3\). This means the line crosses the y - axis at the point \((0,-3)\).

   Step2: Use the slope to find another point

   The slope \(m =-\frac{3}{2}\). The slope is defined as \(\frac{\text{rise}}{\text{run}}\). A slope of \(-\frac{3}{2}\) means that for a run (change in \(x\)) of \(2\) units (we can choose a positive run for simplicity), the rise (change in \(y\)) is \(- 3\) units. Starting from the point \((0,-3)\), if we move \(x = 2\) units to the right (increase \(x\) by 2), then \(y\) will decrease by 3. So the new \(x\) - coordinate is \(0 + 2=2\) and the new \(y\) - coordinate is \(-3-3=-6\). So we have another point \((2,-6)\) on the line.

   Step3: Plot the points and draw the line

   Plot the points \((0,-3)\) and \((2,-6)\) on the coordinate plane. Then, use a straight - edge to draw a line passing through these two points. We can also check with another point. For example, if \(x=-2\), then \(y =-\frac{3}{2}\times(-2)-3=3 - 3 = 0\). So the point \((-2,0)\) is also on the line. Plotting this point and confirming that it lies on the line we drew through \((0,-3)\) and \((2,-6)\) helps to ensure the line is correct.

   To draw the line:

   1. Locate the point \((0,-3)\) on the y - axis (3 units below the origin).
   2. Locate the point \((2,-6)\) (2 units to the right of the y - axis and 6 units below the origin) or \((-2,0)\) (2 units to the left of the y - axis and on the x - axis).
   3. Draw a straight line connecting these points and extend it in both directions.
3. Final answer

   To draw the line \(y =-\frac{3}{2}x-3\), plot the points \((0, - 3)\), \((2,-6)\) (or \((-2,0)\)) and draw a straight line through them.

Respuesta

Question Analysis

OCR Text

trazar la recta.
$y = -\\frac{3}{2}x - 3$

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