Question

Four different linear functions are represented below. Drag the representation of each function into order from greatest y-intercept to least y-intercept.

Answer 1

Answer:

Step-by-step explanation:

A linear function has been given as,

y = $\frac{1}{3}x+5$

Comparing it with the slope intercept equation,

y = mx + b

b = y-intercept = 5

From the graph,

y-intercept = (-2)

From the given table,

For x = 0, f(x) = 3

Therefore, y-intercept = 3

A line passes through two points (-3, -2) and (3, 0),

Slope of the line = $\frac{y_2-y_1}{x_2-x_1}$

                            = $\frac{0+2}{3+3}$

                            = $\frac{1}{3}$

Equation of a line passing through a point (x', y') and slope = m

y - y' = m(x - x')

If the point is (3, 0) and slope = $\frac{1}{3}$

y - 0 = $\frac{1}{3}(x-3)$

y = $\frac{1}{3}x-1$

y-intercept of this line = (-1)

Therefore, decreasing order of the slopes will be,

$5>3>\frac{1}{3}>(-2)$

Order of the functions with slopes from maximum to lease will be,

1). $y=\frac{1}{3}x+5$

2). Function represented by the table.

3). Line passing through (-3, -2) and (3, 0)

4). Function shown in the graph