Question

Two different linear functions are shown below with two points given from each function. Use slope-intercept form or point-slope form to find the equation of each.
Linear Function A
Points: (–5, –2), (–5, 7)
Linear Function B
Points: (7, –5), (–2, –5)

Function A has:


The equation of line A is:


Function B has:


The equation of line B is:

Answer 1

Answer:

A: x = -5

B: y = -5

Step-by-step explanation:

Function A:

(-5, -2), (-5, 7) It's not a function, because for x = -5 we have two different values of y!

The graph is a vertical line x = -5

Function B:

(7, -5), (-2, -5) It's a function.

The graph is a horizontal line y = -5

Answer 2

Answer:

For Linear Function A: x = -5

For Linear Function B: y = -5

Step-by-step explanation:

Function A:

Points : (–5, –2), (–5, 7)

$\left ( x_1,y_1 \right )=(-5, -2)\\\left ( x_2,y_2 \right ) = (-5, 7)$

Slope:

$\frac{y_2-y_1}{x_2-x_1}=\frac{7+2}{-5+5}=\frac{9}{0}$

So, slope is not defined .i.e, equation is of form x = k where k is any real number.

As it passes through point  (-5,-2), so equation is x = -5

Function B:

Points: (7, -5), (-2, -5)

$\left ( x_1,y_1 \right )=(7, -5)\\\left ( x_2,y_2 \right ) = (-2, -5)$

Slope:

$\frac{y_2-y_1}{x_2-x_1}=\frac{-5+5}{-2-7}=\frac{0}{-9}=0$

As slope is zero equation must be of form y = k where k is any real number.

This line passes through point (–2, –5), so equation is y = -5