Write an equation for the linear function f with the values f(0)=-1 and f(3)=4
Will have form
y = m x + b
where b is the slope and b is the value of y when x = 0
so
first the slope m
goes from y = -1 to y = 4
that is 5
goes from x = 0 to x = 3
that is 3
so
m = 5/3
now when x = 0, we already know y = -1 so b = -1
so
y = (5/3) x - 1
or
3 y = 5 x -3
sorry - typo - m is the slope.
To write the equation for the linear function f given the values f(0)=-1 and f(3)=4, we can use the point-slope form of a linear equation, which is:
y - y1 = m(x - x1)
where (x1, y1) represents a point on the line, and m represents the slope of the line.
First, let's find the slope (m) using the given points (0, -1) and (3, 4). The slope is calculated as the change in y divided by the change in x:
m = (y2 - y1) / (x2 - x1)
= (4 - (-1)) / (3 - 0)
= 5 / 3
Now that we have the slope (m), we can choose any one of the two given points to substitute into the point-slope form. Let's use the point (0, -1):
y - (-1) = (5/3)(x - 0)
Simplifying, we have:
y + 1 = (5/3)x
To write it in the standard form, we can multiply both sides of the equation by 3 to eliminate the fraction:
3y + 3 = 5x
Hence, the equation for the linear function f is 3y + 3 = 5x.