Which of the following is an equation of a line that passes through the point (0, 5) and has a negative slope?
y = 5x + 5
y = 5x
y = -5x - 5
y = 5x - 5
y = -5x + 5
clearly a,b,d are out, since they have a positive slope.
Of the other two choices, which passes through (0,5)?
To find the equation of a line that passes through a point and has a given slope, we can use the point-slope form of a linear equation: y - y1 = m(x - x1), where (x1, y1) represents the given point and m represents the slope.
In this case, the given point is (0, 5) and the slope should be negative. Let's substitute these values into the point-slope form:
y - 5 = m(x - 0)
Since the slope (m) is negative, we can rewrite it as -m:
y - 5 = -m(x - 0)
Simplifying the equation further, we have:
y - 5 = -mx
To match it with one of the given options, we can rewrite it such that the term with x comes first:
y = -mx + 5
Comparing this equation with the available options, we can see that the equation that matches is y = -5x + 5. Therefore, the correct option is:
y = -5x + 5