Question

If f ( x ) is a linear function, f ( − 3 ) = − 1 , and f ( 2 ) = − 4 , find an equation for f ( x ) in slope-intercept form.

Answer 1

The equation for f(x) in slope-intercept form is y = (-3/5)x - 14/5.

Step-by-step explanation:

To find the equation for f(x) in slope-intercept form, we need to determine the slope and the y-intercept. We are given two points on the line: (-3, -1) and (2, -4). First, we calculate the slope using the formula:
m = (y2 - y1) / (x2 - x1)
m = (-4 - (-1)) / (2 - (-3))
m = -3 / 5
The slope is -3/5. Next, we can use the point-slope form of a linear equation to find the equation of the line:
y - y1 = m(x - x1)
y - (-1) = (-3/5)(x - (-3))
y + 1 = (-3/5)(x + 3)
y + 1 = (-3/5)x - 9/5
y = (-3/5)x - 9/5 - 1
y = (-3/5)x - 14/5