The equation for line p can be written as y = 9/7x - 9. Line q is perpendicular to line p and passes through (9,-6). What is the equation of line q? Write the equation in slope-intercept form. Write the numbers in the equation as simplified proper fractions, improper fractions, or integers. ______

Question

The equation for line p can be written as y = 9/7x - 9. Line q is perpendicular to line p and passes through (9,-6). What is the equation of line q? Write the equation in slope-intercept form. Write the numbers in the equation as simplified proper fractions, improper fractions, or integers.   ______

Bytelearn · Accepted Answer

Determine Slope of Line p: Determine the slope of line p. The equation of line p is given as y = 9/7x - 9. The slope (m) of a line in the slope-intercept form y = mx + b is the coefficient of x. Therefore, the slope of line p is 9/7.Find Slope of Line q: Find the slope of line q. Since line q is perpendicular to line p, its slope will be the negative reciprocal of the slope of line p. The negative reciprocal of 9/7 is -7/9.Use Point-Slope Form: Use the point-slope form to find the equation of line q. Line q passes through the point (9, -6) and has a slope of -7/9. The point-slope form of the equation of a line is y - y1 = m(x - x1), where m is the slope and (x1, y1) is a point on the line. Plugging in the values, we get y - (-6) = -7/9(x - 9).Simplify Equation: Simplify the equation of line q. Simplifying the equation from the previous step, we get y + 6 = -7/9(x - 9). Distributing the slope on the right side, we get y + 6 = -7/9x + 7. Now, we need to isolate y to get the slope-intercept form.Solve for y: Solve for y to get the slope-intercept form of line q. Subtracting 6 from both sides of the equation y + 6 = -7/9x + 7, we get y = -7/9x + 7 - 6. Simplifying the constant terms, we get y = -7/9x + 1.

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