Find the linear function with the following properties: f(0)=1 and the slope of f equals -3/2
THANK YOU
y=mx+b
1=(-3/2)(0)+b
b=1
y=(-3/2)x+1
To find the linear function with the given properties, we need to use the point-slope form of a linear equation:
y - y1 = m(x - x1)
where m is the slope, and (x1, y1) is a point on the line.
Given that f(0) = 1, we have the point (0,1). The slope is -3/2.
Plugging in these values into the point-slope form, we get:
y - 1 = (-3/2)(x - 0)
Simplifying, we have:
y - 1 = (-3/2)x
Next, to solve for y, we can distribute the -3/2 to the x:
y = (-3/2)x + 1
Therefore, the linear function with f(0) = 1 and a slope of -3/2 is:
f(x) = (-3/2)x + 1
To find the linear function with the given properties, 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.
Given that f(0) = 1, we know that when x = 0, y = 1. This means that the y-intercept (b) of our linear function is 1.
Also, the slope of the function (m) is given as -3/2.
Plugging these values into the slope-intercept form, we have:
y = -3/2x + 1
Therefore, the linear function with the given properties is f(x) = -3/2x + 1.