Answered

Find the best solutions to your problems with the help of IDNLearn.com. Discover prompt and accurate responses from our experts, ensuring you get the information you need quickly.

Find the equation of the line with slope [tex]\(-9\)[/tex] and passing through [tex]\((7, 8)\)[/tex]. Write your equation in point-slope form [tex]\(y - y_1 = m(x - x_1)\)[/tex] and slope-intercept form.

Point-slope form: [tex]\(\square\)[/tex]

Slope-intercept form: [tex]\(\square\)[/tex]

Sagot :

GinnyAnsweridn
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]
Your engagement is important to us. Keep sharing your knowledge and experiences. Let's create a learning environment that is both enjoyable and beneficial. IDNLearn.com is dedicated to providing accurate answers. Thank you for visiting, and see you next time for more solutions.