Question

. Answer each of the following prompts:

(a) Write the point-slope form of a function that has a slope of −3 and passes through the point (11, 2).
(b) Using the point-slope form of the function found in part a, compute the y-intercept of that function by setting x = 0 and solving for y.
(c) Write the slope-intercept form of the function found in part a.

Answer 1

The point-slope form equation is y - 2 = -3(x - 11). The y-intercept is determined by setting x = 0, which gives us the y-intercept (0, 35). The slope-intercept form of the equation is y = -3x + 35.

Step-by-step explanation:

Point-Slope Form and Slope-Intercept Form of a Linear Equation:

The point-slope form of the equation of a straight line with a slope of -3 that passes through the point (11, 2) is written as:

y - 2 = -3(x - 11)

To find the y-intercept, we set x = 0 in the point-slope form:

y - 2 = -3(0 - 11)

y - 2 = 33

y = 35

Therefore, the y-intercept is the point (0, 35).

For the slope-intercept form of the function, we use the standard y = mx + b format, where m is the slope and b is the y-intercept:

y = -3x + 35