To find the equation of the line with a slope of -9 that passes through the point (7, 8), we will write the equation in both point-slope form and slope-intercept form.
### Point-Slope Form
The point-slope form of the equation of a line is given by:
[tex]\[ y - y_1 = m(x - x_1) \][/tex]
Given:
- Slope (m) = -9
- Point (x_1, y_1) = (7, 8)
Substituting the given values into the point-slope form:
[tex]\[ y - 8 = -9(x - 7) \][/tex]
So, the point-slope form of the equation is:
[tex]\[ y - 8 = -9(x - 7) \][/tex]
### Slope-Intercept Form
To convert the point-slope form to the slope-intercept form [tex]\( y = mx + b \)[/tex], we need to distribute the slope and simplify the equation.
Starting with the point-slope form:
[tex]\[ y - 8 = -9(x - 7) \][/tex]
Distribute the slope on the right-hand side:
[tex]\[ y - 8 = -9x + 63 \][/tex]
Next, solve for [tex]\( y \)[/tex] by adding 8 to both sides:
[tex]\[ y = -9x + 63 + 8 \][/tex]
[tex]\[ y = -9x + 71 \][/tex]
So, the slope-intercept form of the equation is:
[tex]\[ y = -9x + 71 \][/tex]
### Summary
- Point-slope form: [tex]\[ y - 8 = -9(x - 7) \][/tex]
- Slope-intercept form: [tex]\[ y = -9x + 71 \][/tex]
