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:

$m=\frac{y_2-y_1}{x_2-x_1}$

Thus, we have:

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

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:

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

Multiply all terms by 4:

$\begin{gathered} 4y+4*7=4*\frac{3}{4}x+6*4 \\ \\ 4y+28=3x+24 \\ \\ \end{gathered}$

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