Question

Which graph models the equation 3x-4y=12

Answer 1

Answer:

Explanation:

The line can be understood as an infinite set of points aligned in a single direction. A line can be expressed by an equation that follows the model y = m * x + b, where "x" e "y" are the variables in a plane. This model is called "slope-intercept form." In this expression m is called the slope of the line and is related to the inclination of the line, and b is the independent term and is the value of the point at which the line cuts to the vertical axis (y axis) in the plane.  In general, the slope represents the variation of y with respect to the variation of x too.

In this case you have the equation: 3*x-4*y=12

So, first of all it is convenient to solve for "y".This means that "y" will be isolated to obtain the "slope-intercept form." For that in first place subtract  3 *x  from both sides of the equation.

3*x-3*x-4*y=12-3*x

-4*y=12-3*x

Then divide each term by  -4

$\frac{-4*y}{-4} =\frac{12}{-4} -\frac{3*x}{-4}$

$y =-3 +\frac{3}{4} *x$

Rewriting in pending-intersection form.

$y =\frac{3}{4} *x-3$

Then the slope is $\frac{3}{4}$ and the value of b (y-intercept) is -3.

So the y-intercept is (0,3).

Now substitute 0 for y to find the x-intercept:

$0=\frac{3}{4} *x-3$

$3=\frac{3}{4} *x-3+3$

$3=\frac{3}{4} *x$

$\frac{3}{\frac{3}{4} } =\frac{\frac{3}{4} }{\frac{3}{4} } *x$

$3* \frac{4}{3} =1*x$

$\frac{12}{3} =x$

4=x

So the x-intercept is (-4,0).

As any line can be plotted using two points, using the intersections in "x" and "y" the equation will be plotted as shown in the attached image.

Answer 2

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