Line v has an equation of y = -10/9x - 3. Perpendicular to line v is line w, which passes through the point (2,3). What is the equation of line w? 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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Line v has an equation of y = -10/9x - 3. Perpendicular to line v is line w, which passes through the point (2,3). What is the equation of line w? 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 v: Determine the slope of line v. The equation of line v is given as y = -10/9x - 3. The slope (m) of a line in the form y = mx + b is the coefficient of x. Therefore, the slope of line v is -10/9.Find slope of line w: Find the slope of line w. Since line w is perpendicular to line v, its slope will be the negative reciprocal of the slope of line v. The negative reciprocal of -10/9 is 9/10.Use point-slope form: Use the point-slope form to find the equation of line w. We have the slope of line w (9/10) and a point through which it passes (2,3). 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) = 9/10(x - 2).Simplify to slope-intercept form: Simplify the equation to slope-intercept form. Starting with (y - 3) = 9/10(x - 2), we distribute the slope on the right side: y - 3 = 9/10 * x - 9/10 * 2 y - 3 = 9/10 * x - 18/10 Now, add 3 to both sides to solve for y: y = 9/10 * x - 18/10 + 3 y = 9/10 * x - 18/10 + 30/10 y = 9/10 * x + 12/10 Simplify the fraction 12/10 to 6/5: y = 9/10 * x + 6/5

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