Finding Equation of Perpendicular Line
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.
