156k views
0 votes
Hello, I need help with this 8th Grade Math Problem. Thank You!

Hello, I need help with this 8th Grade Math Problem. Thank You!-example-1

1 Answer

4 votes

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}

User InfinityGoesAround
by
8.7k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories