Question

tables and graphs. complete both problems A state the start value. state the growth value b write the equation for the linear pattern in the table above. c choose the graph below matching the date in the table.

Answer 1

a) Start value = 1

Growth value = (2/3)

b) Equation for the linear pattern

y = (2/3) x + 1

c) The first graph is the answer. It matches the data in the table.

Step-by-step explanation

The slope and y-intercept form of the equation of a straight line is given as

y = mx + c

where

y = y-coordinate of a point on the line.

m = slope of the line.

x = x-coordinate of the point on the line whose y-coordinate is y.

c = y-intercept of the line.

From the image sent, we can see from the table that the start value (y-intercept, that is, the value of y when x = 0)

From the table, we can see that when x = 0, y = 1

So,

The start value = c = 1

Then, for the growth value, this is the slope of the graph.

For a straight line, the slope of the line can be obtained when the coordinates of two points on the line are known. If the coordinates are (x₁, y₁) and (x₂, y₂), the slope is given as

`Slope=m=\frac{Change\text{ in y}}{Change\text{ in x}}=(y_2-y_1)/(x_2-x_1)`

For this question, we will pick the two extreme values on the table.

(x₁, y₁) and (x₂, y₂) are (-3, -1) and (12, 9)

`\text{Slope = }(9-(-1))/(12-(-3))=(9+1)/(12+3)=(10)/(15)=(2)/(3)`

Slope = m = (2/3)

b) So, we can write the equation

y = mx + c

m = (2/3)

c = 1

y = (2/3) (x) + 1

y = (2x/3) + 1

c) We are then given two graphs to pick which one is correct.

The best way to pick is to check if the values on the table correspond to the points on the line.

(x, y)

(-3, -1)

(0, 1)

(3, 3)

etc.

We can see that it is the first graph that has a line that passes through this points.

Hence, that is our answer.

Hope this Helps!!!