To find the zero of a linear function (the x-intercept), you need to use the slope-intercept form of a linear equation, which is:
y = mx + b
Where:
- y is the dependent variable (in this case, it's the value of the function f(x)).
- x is the independent variable.
- m is the slope of the line.
- b is the y-intercept, which is the point where the line crosses the y-axis (when x = 0).
In your case, you know the function f passes through the point (-4, -3), and you need to find the zero of the function. You also know the slope (m), but you don't have the y-intercept (b) yet.
You can use the point-slope form of a linear equation to find b:
y - y₁ = m(x - x₁)
Using the point (-4, -3):
-3 - (-3) = m(-4 - (-4))
This simplifies to:
0 = m(0)
Since the slope (m) times 0 equals 0, you know that b is equal to -3. So, now you have the equation for the linear function f:
f(x) = mx + b
f(x) = mx - 3
To find the zero of this function, set f(x) equal to 0:
0 = mx - 3
Now, solve for x:
mx = 3
x = 3/m
So, the zero of the function f(x) is x = 3/m, where "m" is the slope of the function.