,Step 1:
First determine the slope-intercept form of the equation of a line.
[tex]\text{Slope = }\frac{y_2-y_1}{x_2-x_1}\text{ = }\frac{y-y_1}{x-x_1}[/tex]
Step 2:
Next, substitute all values to find the equation of a line.
[tex]\begin{gathered} x_1\text{ = }10 \\ y_1\text{ = 4} \\ x_2\text{ = 3} \\ y_2\text{ = 9} \\ \frac{y\text{ - }4}{x\text{ -10}}\text{ = }\frac{9\text{ - 4}}{13\text{ - 10}} \\ \frac{y\text{ - 4}}{x\text{ - 10}}\text{ = }\frac{5}{3} \\ 3y\text{ - 12 = 5x - 50} \\ 3y\text{ - 5x = }-38 \end{gathered}[/tex]
Substitute x and y from each option, any option that results in -38 is the answer.
Final answer
Option C
Let check
3y - 5x = -38
3(14) - 5(16)
42 - 80 = -38
