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A: $($ $14$ , $12$ . $6$ $)$ B: $($ $14$ , $2$ $)$ C: $($ $4$ , $2$ $)$ Find the equations of lines $AB$ , $BC$ , and $AC$ in the diagram.

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Write a quadratic function from its x-intercepts and another point

Full solution

Q. A:

(

14

,

12

.

6

)

B:

(

14

,

2

)

C:

(

4

,

2

)

Find the equations of lines

AB

,

BC

, and

AC

in the diagram.

Calculate slope of line $AB$ : Calculate the slope of line $AB$ . $\newline$ Since $A$ and $B$ have the same $x$ -coordinate, the slope is undefined, and line $AB$ is vertical.
Write equation of line AB: Write the equation of line AB. $\newline$ For a vertical line at $x = 14$ , the equation is $x = 14$ .
Calculate slope of line BC: Calculate the slope of line BC. Use the slope formula $(y_2 - y_1) / (x_2 - x_1)$ with points B $(14,2)$ and C $(4,2)$ . Slope of BC = $(2 - 2) / (14 - 4) = 0 / 10 = 0$ .
Write equation of line BC: Write the equation of line BC. $\newline$ For a horizontal line at $y = 2$ , the equation is $y = 2$ .
Calculate slope of line AC: Calculate the slope of line AC. Use the slope formula with points $A(14,12.6)$ and $C(4,2)$ . Slope of $AC = \frac{12.6 - 2}{14 - 4} = \frac{10.6}{10} = 1.06$ .
Write equation of line AC: Write the equation of line AC using point-slope form. $\newline$ Start with $y - y_1 = m(x - x_1)$ using point A $(14,12.6)$ and slope $1.06$ . $\newline$ $y - 12.6 = 1.06(x - 14)$ .
Simplify equation of line AC: Simplify the equation of line AC. Distribute the slope and add $12.6$ to both sides. $y = 1.06x - 14.84 + 12.6$ . $y = 1.06x - 2.24$ .

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