Question

Which equations and/or functions represent the graphed line? Select three options.

4
.
..6
Х
1

Answer 1

The equations that can represent the graph are y = 1/2x + 2, x - 2y = -4 and x - 2y + 4 = 0

How to calculate the equation of the graph

From the question, we have the following parameters that can be used in our computation:

The linear graph

In the graph, we can see that

Points = (2, 3) and (0, 2)

The equation of a linear graph is represented as

y = mx + c

Where

m = slope

c = y-intercept i.e. y, when x = 0

Using the point (0, 2), we have

c = 2

So, the function becomes

y = mx + 2

Using the point (2, 3), we have

2m + 2 = 3

2m = 1

m = 1/2

So, the function becomes

y = 1/2x + 2

Multiply through by 2

2y = x + 4

Also, we have

x - 2y = -4

Lastly, we have

x - 2y + 4 = 0

Hence, the equations of the graph are y = 1/2x + 2, x - 2y = -4 and x - 2y + 4 = 0

Question

Which equations and/or functions represent the graphed line? Select three options.

x - 2y + 4 = 0

y = 1/5x - 4

y = 1/2x + 2

x - 2y = -4

Answer 2

f(x) = 0.5x + 2

f(x) = 1/2x + 2

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

y - 1 = 0.5(x + 2)

Explanation:

In the figure attached, the graphed line is shown.

The missing options are:

f(x) = 0.2x - 4

f(x) = 0.5x + 2

f(x) = 1/2x + 2

y – 3 = 1/2(x – 2)

y – 1 = 0.5(x + 2)

From the picture, we can see that points (0, 2) and (2, 3) are on the line. Then, the slope of the line is:

m = (3 - 2)/(2 - 0) = 1/2 = 0.5

The y-intercept is (0, 2), or b = 2

Therefore, in the slope y-intercept form, the equation is:

f(x) = mx + b

f(x) = 1/2x + 2 = 0.5x + 2

In the point-slope form, the equations is:

y - y1 = m(x - x1)

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

Using point (-2, 1), in the point-slope form, the equation is:

y - y1 = m(x - x1)

y - 1 = 0.5(x + 2)