Question

Use the slope-intercept form to write an equation of the line that passes through the given point and has the given slope. Use function notation where y =f(x).

(-3,1); m = -2/3
Select one:
a. f(x) = (2/3)x-1
b. f(x) = -(2/3)x-1
c. f(x) = -(2/3)x + 5
d. f(x) = -(2/3)x-3

Answer 1

To write an equation of a line using the slope-intercept form, substitute the given slope and coordinates of the point into the formula f(x) = mx + b and solve for f(x).

Step-by-step explanation:

To write an equation of a line using the slope-intercept form, we need to use the formula: f(x) = mx + b, where m is the slope and b is the y-intercept. In this case, the slope (m) is -2/3, and the point is (-3,1). To find the equation, substitute the values into the formula and solve for f(x).

f(x) = -2/3x + b

Substituting the coordinates of the point (-3,1):

1 = -2/3(-3) + b

Now, solve for b:

1 = 2 + b

b = -1

The equation of the line that passes through the point (-3,1) and has a slope of -2/3 is f(x) = -2/3x - 1.