Line p has an equation of y–3= 1/4 (x+1). Line q is perpendicular to line p and passes through (3, – 6). What is the equation of line q?

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Line p has an equation of y–3=  1/4 (x+1). Line q is perpendicular to line p and passes through (3, – 6). What is the equation of line q?

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Convert to Slope-Intercept Form: Convert the equation of line p to slope-intercept form to find its slope. The equation of line p is given as y–3 = 1/4 (x+1). To convert it to slope-intercept form (y = mx + b), we need to distribute the 1/4 and move the constant term to the other side. y - 3 = 1/4 * x + 1/4 y = 1/4 * x + 1/4 + 3 y = 1/4 * x + 13/4 The slope (m) of line p is 1/4.Find Perpendicular Slope: Determine the slope of line q which is perpendicular to line p. Since line q is perpendicular to line p, its slope will be the negative reciprocal of the slope of line p. The slope of line p is 1/4, so the negative reciprocal is -4 (since the negative reciprocal of 1/4 is -1/(1/4) = -4).Use Point-Slope Form: Use the point-slope form to find the equation of line q. Line q passes through the point (3, –6) and has a slope of -4. The point-slope form 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 slope and the point into the point-slope form, we get: y - (-6) = -4(x - 3) y + 6 = -4x + 12Convert to Slope-Intercept Form: Convert the equation from point-slope form to slope-intercept form. To convert the equation to slope-intercept form (y = mx + b), we need to isolate y on one side of the equation. y + 6 = -4x + 12 y = -4x + 12 - 6 y = -4x + 6 The equation of line q in slope-intercept form is y = -4x + 6.

Line $p$ has an equation of $y-3= \frac{1}{4} (x+1)$ . Line $q$ is perpendicular to line $p$ and passes through $(3, -6)$ . What is the equation of line $q$ ?

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Line $p$ has an equation of $y-3= \frac{1}{4} (x+1)$ . Line $q$ is perpendicular to line $p$ and passes through $(3, -6)$ . What is the equation of line $q$ ?