Question

51B 94730a>121518-106 41086426498y-axisInB) 4x-3y=124What's the equation of the graph shown above?A) 3x - 4y= 4OC) 3x-4y=1OD) 4x-3y=4X-azis6 8 10

Answer 1

From the graph, let's take two points:

(x1, y1) ==> (-8, -7)

(x2, y2) ==> (4, 2)

Let's find the equation of the graph.

To find the equation, let's first find the slope of the line using the slope formula:

`m=(y_2-y_1)/(x_2-x_1)`

Thus, we have:

`\begin{gathered} m=(2-(-7))/(4-(-8)) \\ \\ m=(2+7)/(4+8) \\ \\ m=(9)/(12) \\ \\ m=(3)/(4) \end{gathered}`

Now, apply the point-slope form:

`(y-y_1)=m(x-x_1)`

Where:

m is the slope

(x1, y1) are the coordinates of one point.

Thus, we have:

`\begin{gathered} (y-(-7))=(3)/(4)(x-(-8)) \\ \\ (y+7)=(3)/(4)(x+8) \\ \\ \text{ Apply distributive property:} \\ y+7=(3)/(4)x+(3)/(4)*8 \\ \\ y+7=(3)/(4)x+6 \\ \end{gathered}`

Multiply all terms by 4:

`\begin{gathered} 4y+4*7=4*(3)/(4)x+6*4 \\ \\ 4y+28=3x+24 \\ \\ \end{gathered}`

SOlving further:

`\begin{gathered} 28-24=3x-4y \\ \\ 4=3x-4y \\ \\ 3x-4y=4 \end{gathered}`

Therefore, the equation of the graph is:

3x-4y=4

ANSWER:

(A) 3x - 4y = 4