Which linear equation would produce a y-intercept of (0, -6) and a slope of 2?
A y=2x-6
B y= 2x+6
C y=-6x + 2
D y=-6x-2
The Correct Answer and Explanation is :
The correct answer is A: ( y = 2x – 6 ).
Explanation:
A linear equation is generally expressed in the slope-intercept form:
[
y = mx + b
]
Where:
- m represents the slope of the line,
- b represents the y-intercept, the point where the line crosses the y-axis.
The problem states that the slope is 2 and the y-intercept is (0, -6). This means that when ( x = 0 ), the value of ( y ) is -6.
From the given information:
- The slope ( m = 2 ),
- The y-intercept ( b = -6 ).
Thus, the equation of the line would be:
[
y = 2x – 6
]
Breaking down the options:
- Option A: ( y = 2x – 6 ): This equation has a slope of 2 and a y-intercept of -6, which matches the conditions specified in the question. Therefore, this is the correct equation.
- Option B: ( y = 2x + 6 ): This equation also has a slope of 2, but the y-intercept is +6, not -6. Therefore, this option is incorrect.
- Option C: ( y = -6x + 2 ): In this equation, the slope is -6 (not 2) and the y-intercept is +2 (not -6). Thus, this is incorrect.
- Option D: ( y = -6x – 2 ): This equation has a slope of -6 (not 2) and a y-intercept of -2 (not -6). This is also incorrect.
Summary:
The equation ( y = 2x – 6 ) correctly represents a line with a slope of 2 and a y-intercept of (0, -6). This is the only option that fits both conditions provided in the problem. Therefore, Option A is the correct answer.