A graph of a straight line is displayed on a grid. The line has a steep negative slope, descending from the top right quadrant to the bottom left quadrant. The line passes through the point (0, 0) and has a negative gradient. The x-axis ranges from -5 to 5, and the y-axis from -5 to 5. Each grid line represents one unit.
Identify the graphed linear equation.
Responses
A y = 4x + 1y = 4x + 1
B y = 4x - 1y = 4x - 1
C y = -4x + 1y = -4x + 1
D y = -4x - 1
Identify the graphed linear equation.
Responses
A y = 4x + 1y = 4x + 1
B y = 4x - 1y = 4x - 1
C y = -4x + 1y = -4x + 1
D y = -4x - 1
Answers
Answered by
GPT-4o mini
Given that the line has a steep negative slope and passes through the origin (0, 0), we can derive the linear equation in the slope-intercept form \( y = mx + b \), where \( m \) represents the slope and \( b \) represents the y-intercept.
Since the line passes through the origin (0, 0), we know that the y-intercept \( b = 0 \). This simplifies our equation to \( y = mx \).
The negative slope indicates that as \( x \) increases, \( y \) decreases. Since the slope is described as steep, we can infer that the slope has a relatively large absolute value. Given the options:
- A: \( y = 4x + 1 \) (positive slope, not applicable)
- B: \( y = 4x - 1 \) (positive slope, not applicable)
- C: \( y = -4x + 1 \) (negative slope, but not through the origin)
- D: \( y = -4x - 1 \) (negative slope, but not through the origin)
None of the options appear to fit the equation based on the line's steep negative slope through the origin. However, if we adjust for the y-intercept, we may realize that the correct representation of a steep negative slope from the point (0, 0) should actually be written as \( y = -4x \) to pass through the origin.
Therefore, based on the closest options given (noting that none accurately reflect the exact intercept), the most correct choice for a steep negative slope would involve \( y = -4x \). However, the options provided do not exactly capture that.
If you must select from these options based solely on the negative slope, select **D: y = -4x - 1**, as it has the steep negative slope (even though it has a y-intercept not at the origin as stated).
Since the line passes through the origin (0, 0), we know that the y-intercept \( b = 0 \). This simplifies our equation to \( y = mx \).
The negative slope indicates that as \( x \) increases, \( y \) decreases. Since the slope is described as steep, we can infer that the slope has a relatively large absolute value. Given the options:
- A: \( y = 4x + 1 \) (positive slope, not applicable)
- B: \( y = 4x - 1 \) (positive slope, not applicable)
- C: \( y = -4x + 1 \) (negative slope, but not through the origin)
- D: \( y = -4x - 1 \) (negative slope, but not through the origin)
None of the options appear to fit the equation based on the line's steep negative slope through the origin. However, if we adjust for the y-intercept, we may realize that the correct representation of a steep negative slope from the point (0, 0) should actually be written as \( y = -4x \) to pass through the origin.
Therefore, based on the closest options given (noting that none accurately reflect the exact intercept), the most correct choice for a steep negative slope would involve \( y = -4x \). However, the options provided do not exactly capture that.
If you must select from these options based solely on the negative slope, select **D: y = -4x - 1**, as it has the steep negative slope (even though it has a y-intercept not at the origin as stated).
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