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Find an equation for the line with the given properties. Express your answer using either the general form or he slope-intercept form of the equation of a line. Parallel to the line \( 9 x-y=-9 \); containing the point \( (0,0) \) The equation is (Type an equation. Simplify your answer.)

Ask by Garza Valdez. in the United States
Feb 04,2025

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The equation of the line is \( y = 9x \).

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Mind Expander

To find an equation for a line that is parallel to the line given by \(9x - y = -9\), we first need to determine the slope of the original line. By rearranging it into slope-intercept form (y = mx + b), we get: \[ y = 9x + 9 \] This tells us that the slope (m) of the line is 9. Since parallel lines have the same slope, the slope of our desired line will also be 9. Using the point-slope form of a line, where \(y - y_1 = m(x - x_1)\), and substituting \(m = 9\) and the point \((0, 0)\): \[ y - 0 = 9(x - 0) \] Simplifying this gives us: \[ y = 9x \] Thus, the equation of the line can also be expressed in general form as \(9x - y = 0\). The final answer is: \(y = 9x\) or \(9x - y = 0\)

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