A line crosses the y-axis at (0,4) and has a slope of -2. Find an equation for this line.
Responses
A. y = -4x + 2
B. y = -2x - 4
C. y = 2x + 4
D. y = -2x + 4
D. y = -2x + 4
To find an equation for this line, we can use the slope-intercept form: y = mx + b, where m is the slope and b is the y-intercept.
From the given information, we know that the line crosses the y-axis at (0,4) and has a slope of -2.
So, the slope (m) is -2, and the y-intercept (b) is 4.
Substituting these values into the slope-intercept form, we have:
y = -2x + 4
Therefore, the correct equation for this line is option D: y = -2x + 4.
To find an equation for a line, we need to use the slope-intercept form of a linear equation, which is y = mx + b, where m is the slope of the line, and b is the y-intercept (the point where the line intersects the y-axis).
In this case, we are given that the line crosses the y-axis at (0,4), which means the y-intercept is 4. We are also given that the slope of the line is -2.
Now, we can substitute the values we have into the slope-intercept form to find the equation of the line.
Using the values m = -2 and b = 4, we get:
y = -2x + 4
Therefore, the correct equation for the line is y = -2x + 4.
So, the answer is option D: y = -2x + 4.