Question - Finding Equation of Perpendicular Line
Solution:
To find the equation of line h, which is perpendicular to line g, we will follow these steps:1. Identify the slope of line g.2. Determine the slope of line h.3. Use the point-slope form to create the equation of line h.4. Convert the equation into slope-intercept form.The equation for line g is given as $$ y = \frac{3}{10}x - 8 $$. The slope of line g is the coefficient of x, which is $$ \frac{3}{10} $$.Lines that are perpendicular to each other have slopes that are negative reciprocals. Therefore, if the slope of line g is $$ \frac{3}{10} $$, the slope of line h will be its negative reciprocal, which is $$ -\frac{10}{3} $$.Now, we know that line h has a slope of $$ -\frac{10}{3} $$ and it passes through the point (3, -9). We can use the point-slope form of the equation to find the equation of line h:$$ y - y_1 = m(x - x_1) $$Substitute m (slope) with $$ -\frac{10}{3} $$ and $$ (x_1, y_1) $$ with (3, -9):$$ y - (-9) = -\frac{10}{3}(x - 3) $$Simplify and solve for y to get the equation in slope-intercept form:$$ y + 9 = -\frac{10}{3}x + 10 $$$$ y = -\frac{10}{3}x + 10 - 9 $$$$ y = -\frac{10}{3}x + 1 $$Therefore, the equation of line h in slope-intercept form is $$ y = -\frac{10}{3}x + 1 $$, with the numbers in the equation as simplified improper fractions or integers.
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