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What is the slope-intercept form of a line given a slope of 3 and a y-intercept of -4?

Ask by Gough Hills. in India
Jan 21,2025

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Tutor-Verified Answer

Answer

The slope-intercept form of the line is \( y = 3x - 4 \).

Solution

The **slope-intercept form** of a line is expressed as: \[ y = mx + b \] Where: - \( m \) is the **slope** of the line. - \( b \) is the **y-intercept** (the point where the line crosses the y-axis). Given: - **Slope (\( m \))** = 3 - **Y-intercept (\( b \))** = -4 Plugging these values into the slope-intercept form: \[ y = 3x - 4 \] **So, the equation of the line is:** \[ y = 3x - 4 \]

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Extra Insights

The slope-intercept form of a line is expressed as y = mx + b, where m is the slope and b is the y-intercept. With a slope of 3 and a y-intercept of -4, you can plug in these values to get the equation: y = 3x - 4. Now you have a beautifully crafted linear equation ready for graphing! In practical terms, this means that for every increase of 1 unit in x, y will increase by 3 units. Feeling adventurous? You can plot this line on a graph, starting from the y-intercept at (0, -4) and then moving up 3 units for each step to the right. You'll have a straight line that represents all the solutions to this equation—how cool is that?

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