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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

Real Tutor Solution

Tutor-Verified Answer

Answer

The equation of the line is \( y = 3x - 2 \).

Solution

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:** \[ y = 3x - 2 \]

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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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