Question

Which steps should be used to graph the equation y – 4 = y minus 4 equals StartFraction one-third EndFraction left-parenthesis x plus 2 right-parenthesis.(x + 2)?

Answer 1

Answer:

The steps are are explained below.

Step-by-step explanation:

Given:

The equation of the line is given as:

$y-4=\frac{1}{3}(x+2)$

The above equation is in point-slope form $y-y_1=m(x-x_1)$.

Therefore, on comparing, we get

$x_1=-2,y_1=4,m=\frac{1}{3}$

So, the slope is one-third and point is (-2,4).

Now, following are steps for plotting the graph:

i. Plot the point (-2,4).

ii. Since the slope is one-third, it means we need to move 3 units to right from the point (-2,4) and then 1 unit up. So, after translating 3 units right and 1 unit up we mark the second point which is $(-2+3,4+1)\rightarrow )(1,5)$.

iii. Draw a line passing through the points (-2,4) and (1,5) to get the graph of the line

Thus, the graph is drawn below.

Answer 2

The graph of the equation $y-4 = \frac{1}{3} (x+2)$ was plotted by determining two of its points.

Given equation is:

$y-4 = \frac{1}{3} (x+2)$.....(1)

Which is an equation of a straight line.

What is the equation of a straight line?

The equation of a straight line is,

$y = mx+c$

Where m = slope of the line.

In order to get the graph of the given equation, we need to find at least two points satisfying the equation $y-4 = \frac{1}{3} (x+2)$

Put x=0 in the above equation (1)

So, $y-4 = \frac{1}{3} (0+2)$

y = 14/3

The point will be (0, 14/3)

Put y=0 in the above equation (1)

So, $0-4 = \frac{1}{3} (x+2)$

x= -14

The point will be (-14,0)

So, we got two points (0, 14/3) and (-14,0)

In order to get the required graph, we need to mark these points on coordinate axes and join these points.

Find the attached diagram to understand better

Thus, the graph of the equation $y-4 = \frac{1}{3} (x+2)$ was plotted by determining two of its points.

To get more about the straight-line visit:

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