Question

what are the values of a and b and what is the equation for the line?explain how you determine the asnwer.

Answer 1

a = 1

b = 6

y = 1/3 x + 1

Step-by-step explanation:

To find a and b, we need to find the slope of the equation using any two points on the line

Slope formula:

`m\text{ = }(y_2-y_1)/(x_2-x_1)`

Using points: (3, 2) and (12, 5):

`\begin{gathered} x_1=3,y_1=2,x_2=12,y_2\text{ = }5 \\ m\text{ = }(5-2)/(12-3)=(3)/(9) \\ m\text{ =slope = 1/3} \end{gathered}`

To get a, we would use points (0, a) and (3, 2) in the slope formula:

`\begin{gathered} m\text{ =}(2-a)/(3-0) \\ (1)/(3)=(2-a)/(3) \\ 3(1)\text{ = 3(2-a)} \\ 3\text{ = 6 - 3a} \\ 3\text{ - 6 = -3a} \\ -3\text{ = -3a} \\ \frac{-3}{-3\text{ }}=(-3a)/(-3) \\ a\text{ = 1} \end{gathered}`

To get b, we would use points (3, 2) and (b, 3) in the slope formula:

`\begin{gathered} m\text{ = }(3-2)/(b-3) \\ (1)/(3)\text{= }(1)/(b-3) \\ 3(1)\text{ = 1(b-3)} \\ 3\text{ = b - 3} \\ 3+3\text{ = b} \\ b\text{ = 6} \end{gathered}`

The equation of line: y = mx + c

m = 1/3

c = y-intercept

The y-intercept is the value of y when the line crosses the y-axis:

The value of y = a = 1

c = y-intercept = 1

Inserting the values into the equation:

y = 1/3 x + 1