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In Mathematics / High School | 2025-07-05

If you wanted to make the graph of $y=6 x+7$ less steep, which equation could you use?
A. $y=10 x+7$
B. $y=2 x+7$
C. $y=-6 x+7$
D. $y=6 x+4

Asked by alijahfrost513

Answer (1)

The steepness of a line is determined by the absolute value of its slope.
The given equation y = 6 x + 7 has a slope of 6.
We need to find an equation with a slope whose absolute value is less than 6.
Among the options, y = 2 x + 7 has a slope of 2, which satisfies the condition. Therefore, the answer is B ​ .

Explanation

Understanding the Problem The problem asks us to identify which equation, when graphed, would be less steep than the line y = 6 x + 7 . The steepness of a line is determined by the absolute value of its slope.

Identifying the Slope The given equation, y = 6 x + 7 , is in slope-intercept form, y = m x + b , where m represents the slope and b represents the y-intercept. In this case, the slope is 6. We need to find an equation among the options with a slope whose absolute value is less than ∣6∣ = 6 .

Comparing Slopes Let's examine each option:


A. y = 10 x + 7 : The slope is 10, and ∣10∣ = 10 , which is greater than 6. B. y = 2 x + 7 : The slope is 2, and ∣2∣ = 2 , which is less than 6. C. y = − 6 x + 7 : The slope is -6, and ∣ − 6∣ = 6 , which is equal to 6. D. y = 6 x + 4 : The slope is 6, and ∣6∣ = 6 , which is equal to 6.

Determining the Answer Since we are looking for an equation with a slope whose absolute value is less than 6, option B, y = 2 x + 7 , is the correct choice because its slope is 2, and ∣2∣ < 6 .

Examples
Understanding the steepness of a line is crucial in many real-world applications. For example, when designing roads or ramps, engineers need to consider the slope to ensure safety and ease of use. A less steep slope means a gentler incline, making it easier for vehicles or people to climb. In finance, the slope of a trend line on a stock chart can indicate the rate of increase or decrease in price, helping investors make informed decisions. This concept applies to various fields, from architecture to economics, where understanding rates of change is essential.

Answered by GinnyAnswer | 2025-07-05

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