Write an equation for the linear function f with the given values.
f(4)=-8, f(-3)=1
I thought it was (4,-8) and (-3,1)...O_O
To write an equation for the linear function f, we need to find the slope (m) and the y-intercept (b).
We have two points: (4, -8) and (-3, 1).
First, let's find the slope (m) using the formula:
m = (y2 - y1) / (x2 - x1)
Using the points (4, -8) and (-3, 1), we have:
m = (1 - -8) / (-3 - 4)
m = 9 / -7
Next, we can use the point-slope form of a linear equation to write the equation:
y - y1 = m(x - x1)
Using the point (4, -8) and the slope 9/ -7, we have:
y - (-8) = (9 / -7)(x - 4)
y + 8 = (9 / -7)(x - 4)
Simplifying the equation, we multiply through by -7 to get rid of the fraction:
-7(y + 8) = 9(x - 4)
-7y - 56 = 9x - 36
Finally, we can rearrange the equation to get the standard form:
9x + 7y = -20
So, the equation for the linear function f is 9x + 7y = -20.
To write an equation for a linear function, we need to determine the slope and y-intercept.
First, let's find the slope:
We have two points that lie on the line: (4, -8) and (-3, 1).
The slope of a line passing through two points (x1, y1) and (x2, y2) is given by the formula:
slope = (y2 - y1) / (x2 - x1)
Substituting the coordinates of the two points, we get:
slope = (1 - (-8)) / (-3 - 4) = 9 / (-7) = -9/7
Now, let's find the y-intercept:
We can use either of the two points. Let's use (4, -8).
The equation of a line in slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept.
Substituting the slope and the coordinates of the point (4, -8), we have:
-8 = (-9/7)(4) + b
Multiplying -9/7 by 4, we get:
-8 = -36/7 + b
To isolate b, we can simplify the equation further:
-8 + 36/7 = b
-56/7 + 36/7 = b
-20/7 = b
So, the y-intercept is -20/7.
Therefore, the equation of the linear function f is:
f(x) = -9/7 * x - 20/7
so you have two points, (-8,4) and (-3,1)
slope = (1-4)/(-3+8) = -3/5
then y-1 = (-3/5)(x+3)
y = (-3/5)x -9/5 + 1
y = (-3/5)x - 4/5