Write an equation in slope-intercept form for the line with slope 43 and y -intercept −4 .
The correct answer and explanation is:
Correct Answer:
The equation in slope-intercept form is: y=43x−4y = 43x – 4
Explanation (Approximately 300 words):
To write the equation of a line in slope-intercept form, we use the general formula: y=mx+by = mx + b
Where:
- yy and xx are variables representing coordinates on the line.
- mm is the slope of the line.
- bb is the y-intercept, which is the point where the line crosses the y-axis.
In this problem, the slope mm is given as 43, and the y-intercept bb is given as −4.
Step-by-Step Process:
- Identify the values given:
- Slope m=43m = 43
- Y-intercept b=−4b = -4
- Substitute these values into the slope-intercept form equation:
y=mx+by = mx + b y=43x−4y = 43x – 4
That’s it! This is the equation of the line.
What Does This Mean?
- The slope 4343 tells us that for every 1 unit increase in xx, the value of yy increases by 43 units. This line is very steep and rises quickly from left to right.
- The y-intercept −4-4 means the line crosses the y-axis at the point (0,−4)(0, -4).
Why This Matters:
Slope-intercept form is useful in algebra and real-world applications like graphing, trend analysis, and making predictions. For example, if this line represented a business’s revenue over time, a steep slope like 43 would indicate rapid growth. The y-intercept could represent a starting loss or investment of $4, depending on the context.
In summary, by knowing the slope and the y-intercept, we can construct the entire linear equation and understand its behavior on a graph.