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y+3=-12(x-10) give me 7 things u know about this question

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Sure! Here are seven things I know about the equation \(y + 3 = -12(x - 10)\):

  1. Form of the Equation: This equation is in point-slope form, which is useful for finding the slope of a line and the coordinates of a specific point on that line.

  2. Slope: The slope of the line is \(-12\). This indicates that for every unit increase in \(x\), \(y\) decreases by 12 units.

  3. Point of Interest: The point \((10, -3)\) lies on the line. This point is derived from setting \(x = 10\) in the equation, which simplifies \(y + 3 = 0\), giving \(y = -3\).

  4. Intercept Calculation: To find the \(y\)-intercept, set \(x = 0\). Plugging in \(x = 0\) into the equation yields \(y + 3 = -12(0 - 10)\) or \(y + 3 = 120\), which simplifies to \(y = 117\). Thus, the \(y\)-intercept is \((0, 117)\).

  5. x-intercept Calculation: To find the \(x\)-intercept, set \(y = 0\). Solving \(0 + 3 = -12(x - 10)\) gives \(3 = -12x + 120\) or \(12x = 117\), yielding \(x = 9.75\) or \((9.75, 0)\).

  6. Graph Representation: The line represented by this equation would slope downward due to the negative slope. The steepness of the line can be visualized, indicating a strong negative correlation between \(x\) and \(y\).

  7. Transformation: The equation represents a line that has been translated vertically downward by 3 units and horizontally to the right by 10 units from the original line \(y = -12x\).

These points provide a comprehensive understanding of the behavior, properties, and positioning of the line described by the equation \(y + 3 = -12(x - 10)\).

without all that give me some easy things u know 8 things

Sure! Here are eight straightforward points about the equation \(y + 3 = -12(x - 10)\):

  1. Equation Type: It’s a linear equation.

  2. Slope: The slope is \(-12\).

  3. Key Point: A specific point on the line is \((10, -3)\).

  4. Y-intercept: The line crosses the y-axis at \(y = 117\) when \(x = 0\).

  5. X-intercept: The line crosses the x-axis at \(x = 9.75\) when \(y = 0\).

  6. Negative Slope: The line slopes downward as you move from left to right.

  7. Graph: The line represents a straight line in a coordinate plane.

  8. Rearrangement: The equation can be rearranged to the slope-intercept form \(y = -12x + 117\).