Pregunta
Write the equation of a line in slope-intercept form that has a slope of 3 and passes through the point (2, 4).
Ask by Kelly Barker. in South Africa
Jan 21,2025
Solución de tutoría real
Respuesta verificada por el tutor
Responder
The equation of the line is \( y = 3x - 2 \).
Solución
To write the equation of a line in **slope-intercept form** (`y = mx + b`), where:
- `m` is the slope
- `b` is the y-intercept
**Given:**
- Slope (`m`) = 3
- The line passes through the point (2, 4)
**Steps to find the equation:**
1. **Start with the slope-intercept form:**
\[
y = mx + b
\]
2. **Substitute the known slope (`m = 3`) into the equation:**
\[
y = 3x + b
\]
3. **Use the given point (2, 4) to solve for `b`:**
\[
4 = 3(2) + b
\]
\[
4 = 6 + b
\]
\[
b = 4 - 6
\]
\[
b = -2
\]
4. **Write the final equation with the calculated y-intercept:**
\[
y = 3x - 2
\]
**Final Answer:**
\[
y = 3x - 2
\]
Revisado y aprobado por el equipo de tutoría de UpStudy
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Simplifique esta solución The Deep Dive
To write the equation of a line in slope-intercept form (y = mx + b), start with the slope (m), which is given as 3. Now, use the point (2, 4) to find the y-intercept (b). Plugging the coordinates into the equation gives us 4 = 3(2) + b. Solving for b, we get 4 = 6 + b, leading to b = -2. Therefore, the equation is y = 3x - 2. To confirm your solution, you can graph the line. Start at the y-intercept (0, -2) and use the slope to find other points: from (0, -2), move up 3 units and right 1 unit to reach (1, 1). Continuing this process will help you visualize and check if the line accurately represents the equation derived using the slope and point provided!
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