Question
\( 1 \leftarrow \) Use the given conditions to write an equation for the line in point-slope form and slope-intercept form. Slope \( =-9 \), passing through \( (-8,-8) \) \( y+8=-9(x+8) \) (Simplity your answer. Use integers or fractions for any numbers in the equation.) Type the slope-intercept form of the line. \( \square \) (Simplify your answer. Use integers or fractions for any numbers in the equation.)
Ask by Bob Rojas. in the United States
Feb 26,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The slope-intercept form of the line is \( y = -9x - 80 \).
Solution
We are given a slope of –9 and a point (–8, –8). The point‐slope form is:
y + 8 = –9(x + 8)
To convert to slope-intercept form (y = mx + b), distribute –9 on the right side:
y + 8 = –9x – 72
Then, subtract 8 from both sides:
y = –9x – 72 – 8
Simplify:
y = –9x – 80
Thus, the slope-intercept form of the line is: y = –9x – 80.
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Simplify this solution Bonus Knowledge
To write the equation in point-slope form, we start with the formula \( y - y_1 = m(x - x_1) \), where \( m \) is the slope and \( (x_1, y_1) \) is the point. Given \( m = -9 \) and the point \( (-8, -8) \), we have: \[ y + 8 = -9(x + 8) \] Now, to convert this into slope-intercept form \( y = mx + b \), we distribute and simplify: \[ y + 8 = -9x - 72 \] Subtract 8 from both sides: \[ y = -9x - 80 \] So, the slope-intercept form of the line is: \[ y = -9x - 80 \] Make sure to check your calculations to avoid small mistakes, like distributing the slope or combining like terms incorrectly! It’s easy to slip on signs with negative numbers.
