Pregunta
Write the equation of a line in slope-intercept form with a slope of 3 that passes through the point (2, 5).
Ask by Grant Chambers. in the United States
Jan 23,2025
Solución de tutoría real
Respuesta verificada por el tutor
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The equation of the line is \( y = 3x - 1 \).
Solución
To find the equation of a line in **slope-intercept form**, which is given by:
\[ y = mx + b \]
where:
- \( m \) is the slope
- \( b \) is the y-intercept
**Given:**
- Slope (\( m \)) = 3
- The line passes through the point (2, 5)
**Steps to find \( b \):**
1. Plug the slope and the coordinates of the given point into the equation:
\[ 5 = 3(2) + b \]
2. Solve for \( b \):
\[ 5 = 6 + b \]
\[ b = 5 - 6 \]
\[ b = -1 \]
**Therefore, the equation of the line is:**
\[ y = 3x - 1 \]
Revisado y aprobado por el equipo de tutoría de UpStudy
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Simplifique esta solución Bonus Knowledge
To write the equation of a line in slope-intercept form (y = mx + b), start with the slope (m) of 3. You can use the point (2, 5) to find the y-intercept (b). Plugging in the values into the equation gives us 5 = 3(2) + b. Simplifying this, you get 5 = 6 + b, which leads to b = -1. Therefore, the equation of the line is y = 3x - 1. When working with slope-intercept form, one common mistake is forgetting to adjust the y-intercept after plugging in the coordinates of the point. Always check your calculations to ensure you correctly solve for b!
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