The equation for line f can be written as y = 9/5x - 2. Perpendicular to line f is line g, which passes through the point (5,-3). What is the equation of line g? Write the equation in slope-intercept form. Write the numbers in the equation as simplified proper fractions, improper fractions, or integers. ______

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The equation for line f can be written as y = 9/5x - 2. Perpendicular to line f is line g, which passes through the point (5,-3). What is the equation of line g? 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 f: Determine the slope of line f. The equation of line f is given as y = 9/5x - 2. The slope (m) of a line in the slope-intercept form y = mx + b is the coefficient of x. Therefore, the slope of line f is 9/5.Find slope of line g: Find the slope of line g. Since line g is perpendicular to line f, its slope will be the negative reciprocal of the slope of line f. The negative reciprocal of 9/5 is -5/9. Therefore, the slope of line g is -5/9.Use point-slope form: Use the point-slope form to find the equation of line g. We have the slope of line g (-5/9) and a point through which it passes (5,-3). The point-slope form of a line is y - y1 = m(x - x1), where m is the slope and (x1, y1) is the point on the line. Plugging in the values, we get y - (-3) = -5/9(x - 5).Simplify to slope-intercept form: Simplify the equation to slope-intercept form. First, distribute the slope on the right side: y + 3 = -5/9x + (5/9)*5. Simplify the constant term: y + 3 = -5/9x + 25/9. Now, subtract 3 from both sides to get y by itself: y = -5/9x + 25/9 - 27/9. Combine the constant terms: y = -5/9x - 2/9.

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