A line crosses the y-axis at (0,4) and has a slope of -2. Find an equation for this line.
Responses
A y = 2x + 4y = 2x + 4
B y = -2x + 4y = -2x + 4
C y = -2x - 4y = -2x - 4
D y = -4x + 2
The correct equation for this line is B) y = -2x + 4.
In order to find an equation for the line, we need to use the slope-intercept form: y = mx + b, where m is the slope and b is the y-intercept.
Given that the line crosses the y-axis at (0,4) and has a slope of -2, we can substitute these values into the equation.
Using the point (0,4) to find the y-intercept, we have:
4 = -2(0) + b
4 = b
Now we have the y-intercept, b=4. Plugging this back into the slope-intercept form, we have:
y = -2x + 4
So, the correct equation for this line is y = -2x + 4.
To find the equation for the given line, we need to use the slope-intercept form of a line: y = mx + b, where m represents the slope and b represents the y-intercept.
In this case, the slope is given as -2, and the line crosses the y-axis at (0,4). The point (0,4) represents the y-intercept, which is the value of y when x is 0.
So, the y-intercept (b) is 4, and the slope (m) is -2.
Plugging the values of m and b into the slope-intercept form of a line, we get:
y = -2x + 4
Therefore, the equation for the given line is y = -2x + 4.
So, the correct answer is D: y = -2x + 4.