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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 :

GinnyAnswer
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]
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