The equation for line g can be written as y = 3/10x - 8. Perpendicular to line g is line h, which passes through the point (3,-9). What is the equation of line h? 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 g can be written as y = 3/10x - 8. Perpendicular to line g is line h, which passes through the point (3,-9). What is the equation of line h? 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 g: Determine the slope of line g. The equation of line g is given as y = 3/10x - 8. The slope (m) of a line in the slope-intercept form y = mx + b is the coefficient of x. Therefore, the slope of line g is 3/10.Find slope of line h: Find the slope of line h. Since line h is perpendicular to line g, its slope will be the negative reciprocal of the slope of line g. The negative reciprocal of 3/10 is -10/3.Use point-slope form: Use the point-slope form to find the equation of line h. Line h passes through the point (3,-9) and has a slope of -10/3. 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 values, we get y - (-9) = -10/3(x - 3).Simplify equation of line h: Simplify the equation of line h. First, distribute the slope on the right side of the equation: y + 9 = -10/3(x - 3). Next, distribute -10/3 inside the parentheses: y + 9 = -10/3x + 10. Then, subtract 9 from both sides to get the equation in slope-intercept form: y = -10/3x + 10 - 9. Finally, simplify the constant term: y = -10/3x + 1.

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