Question
Use the given conditions to write an equation for the line in point-slope form and slope-intercept form. Passing through \( (-4,-1) \) and \( (4,11) \) Type the point-slope form of the equation of the line. \( y+1=\frac{3}{2}(x+4) \) (Use integers or simplified fractions for any numbers in the equation.) Type the slope-intercept form of the equation of the line. \( \square \) (Use integers or simplified fractions for any numbers in the equation.)
Ask by Fuentes Haynes. in the United States
Feb 28,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The slope-intercept form of the equation is \( y = \frac{3}{2}x + 5 \).
Solution
We start with the point-slope form already given:
y + 1 = (3/2)(x + 4)
To convert this to slope-intercept form, solve for y:
1. Distribute (3/2) on the right side:
y + 1 = (3/2)x + (3/2) × 4
2. Simplify (3/2) × 4:
(3/2) × 4 = 6
3. Substitute the value back into the equation:
y + 1 = (3/2)x + 6
4. Isolate y by subtracting 1 from both sides:
y = (3/2)x + 6 – 1
y = (3/2)x + 5
Thus, the slope-intercept form of the equation is:
y = (3/2)x + 5
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Simplify this solution Extra Insights
To find the slope-intercept form of the equation, we first need to calculate the slope (m) using the points given. The slope (m) is calculated as: \[ m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{11 - (-1)}{4 - (-4)} = \frac{12}{8} = \frac{3}{2} \] Now, using the point-slope form provided: \[ y + 1 = \frac{3}{2}(x + 4) \] To convert this into slope-intercept form (y = mx + b), we can expand and simplify: 1. Distribute \( \frac{3}{2} \): \[ y + 1 = \frac{3}{2}x + 6 \] 2. Subtract 1 from both sides: \[ y = \frac{3}{2}x + 5 \] So the slope-intercept form of the equation of the line is: \[ y = \frac{3}{2}x + 5 \]
