A line crosses the y-axis at (0,4) and has a slope of -2. Find an equation for this line.
A. y=2x+4
B. y=-2x+4
C. y= -2x-4
D. y = -4x+2
To find the equation of a line, we need to use the slope-intercept form, which is 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), we know that the y-intercept is 4.
The slope of the line is given as -2.
Therefore, the equation for this line is y = -2x + 4.
So the correct answer is B. y = -2x + 4.
To find an equation for the given line that crosses the y-axis at (0,4) and has a slope of -2, we can use the slope-intercept form of a linear equation: y = mx + b, where m is the slope and b is the y-intercept.
In this case, the slope (m) is -2, and the y-intercept is the point (0,4).
Substituting these values into the slope-intercept form, we have:
y = -2x + b
To find the value of b, we substitute the coordinates (0,4) into the equation:
4 = -2(0) + b
4 = 0 + b
b = 4
Therefore, the equation for the line is:
y = -2x + 4
Hence, the answer is A. y = -2x + 4.
To find the equation for the line, we can use the slope-intercept form, which is given by y = mx + b, where m is the slope of the line 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 the values into the slope-intercept form:
y = -2x + b
Now, we need to find the value of b, which is the y-intercept. We know that the line passes through the point (0,4). So, we can substitute x=0 and y=4 into the equation:
4 = -2(0) + b
4 = 0 + b
b = 4
Now that we have the value of b, we can substitute it back into the equation:
y = -2x + 4
Therefore, the equation for the line is y = -2x + 4.
The correct answer is B. y = -2x + 4.