Step 1;
To find the slope of a line, pick two points from the line and find the slope.
Points ( 2, 1 ) , (10 , 13 ) { Reason because the two points have both x and y coordinates)
Step 2
[tex]\begin{gathered} Slope\text{ formula m = }\frac{y_2-y_1}{x_2-x_1} \\ x_1\text{ = 2} \\ y_1=1_{} \\ x_2\text{ = 10} \\ y_2\text{ = 13} \\ m\text{ = }\frac{13\text{ - 1}}{10\text{ - 2}} \\ \text{m = }\frac{12}{8} \\ m\text{ = }\frac{3}{2} \end{gathered}[/tex]
The slope of the line = 3/2
Step 3:
Equation of the line:
To find the equation of a line, use two-point forms equation of a line
[tex]\begin{gathered} \frac{y-y_1}{x-x_1\text{ }}\text{ = }\frac{y_2-y_1}{x_2-x_1} \\ \frac{y\text{ - 1}}{x\text{ - 2}}\text{ = }\frac{13\text{ - 1}}{10\text{ - 2}} \\ \frac{\text{y - 1}}{x\text{ - 2}}\text{ = }\frac{3}{2} \\ 2(y\text{ - 1) = 3(x - 2)} \\ 2y\text{ - 2 = 3x - 6} \\ 2y\text{ = 3x - 6 + 2} \\ \text{2y = 3x - 4} \end{gathered}[/tex]
Step 4:
To find b, plug x = 6 and y = b in the equation of a line formula.
[tex]\begin{gathered} 2y\text{ = 3x - 4} \\ 2b\text{ = 3}\times\text{6 - 4} \\ 2b\text{ = 18 - 4} \\ 2b\text{ = 14} \\ b\text{ = }\frac{14}{2}\text{ = 7} \\ \text{b = 7} \end{gathered}[/tex]
Step 5
To find a, plug x = a and y = 10 in the equation of a line formula.
[tex]\begin{gathered} 2y\text{ = 3x - 4} \\ 3\text{ }\times\text{ 10 = 3a - 4} \\ 30\text{ = 3a - 4} \\ 3a\text{ = 30 + 4} \\ 3a\text{ = 34} \\ \text{a = }\frac{34}{3} \end{gathered}[/tex]
