Question

Hello, I need help with this 8th Grade Math Problem. Thank You!

Answer 1

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

`\begin{gathered} Slope\text{ formula m = }(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 = }(12)/(8) \\ m\text{ = }(3)/(2) \end{gathered}`

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

`\begin{gathered} \frac{y-y_1}{x-x_1\text{ }}\text{ = }(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{ = }(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}`

Step 4:

To find b, plug x = 6 and y = b in the equation of a line formula.

`\begin{gathered} 2y\text{ = 3x - 4} \\ 2b\text{ = 3}*\text{6 - 4} \\ 2b\text{ = 18 - 4} \\ 2b\text{ = 14} \\ b\text{ = }(14)/(2)\text{ = 7} \\ \text{b = 7} \end{gathered}`

Step 5

To find a, plug x = a and y = 10 in the equation of a line formula.

`\begin{gathered} 2y\text{ = 3x - 4} \\ 3\text{ }*\text{ 10 = 3a - 4} \\ 30\text{ = 3a - 4} \\ 3a\text{ = 30 + 4} \\ 3a\text{ = 34} \\ \text{a = }(34)/(3) \end{gathered}`