Question

the table shows some ordered pairs that are on a line. the slope of the line is \\(\frac{3}{4}\\). what is the value of the missing \\(x\\)-coordinate for this table? show your work either algebraically, or by creating a graph to figure out the slope.\
\

\\(x\\)	\\(y\\)	\
----	----	\
-8	-5	\
?	7	\

\
(enter your response here)

Explanation:

Step1: Recall slope formula

Let the missing $x$-coordinate be $x_2$. The slope formula is $m=\frac{y_2-y_1}{x_2-x_1}$, where $m=\frac{3}{4}$, $(x_1,y_1)=(-8,-5)$, $(x_2,y_2)=(x_2,7)$.

Step2: Substitute values into formula

$\frac{3}{4}=\frac{7-(-5)}{x_2-(-8)}$
Simplify numerator: $7-(-5)=12$, denominator: $x_2+8$
$\frac{3}{4}=\frac{12}{x_2+8}$

Step3: Cross-multiply to solve for $x_2$

$3(x_2+8)=4\times12$
$3x_2+24=48$

Step4: Isolate $x_2$

$3x_2=48-24$
$3x_2=24$
$x_2=\frac{24}{3}=8$

Answer:

$8$