Question

Which shows the graph of x – 4y =–4? A coordinate plane with a line passing through (0, negative 4) and (1, 0). A coordinate plane with a line passing through (negative 4, negative 2), (0, negative 1) and (4, 0). A coordinate plane with a line passing through (negative 2, negative 4), (negative 1, 0) and (0, 4). A coordinate plane with a line passing through (negative 4, 0) and (0, 1).

Answer 1

Answer:

A coordinate plane with a line passing through (negative 4, 0) and (0, 1).

Step-by-step explanation:

Values of x and y are satisfied on these coordinates.

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Answer 2

Answer:

The given equation represents a plane with a line passing through the coordinates (-4, 0), (0, 1) and (4, 2).

Step-by-step explanation:

Given a linear equation, $x -4y =-4$

• Linear equation in slope-intercept form is given the form of

        $y = mx+c$

• where $m$ and $c$ are the constants that defines the line of slope $m$ that contains the point $(0,c)$ on the y-axis, which is called as y-intercept.

Writing the given equation in the standard slope-intercept form

$x-4y = -4\implies -4y=-x-4$

                    $\implies 4y=x+4\implies y=\dfrac{x}{4}+\dfrac{4}{4}$

                    $\implies y=\dfrac{1}{4}x+1$

Comparing this equation with the standard form $y = mx + c$,

the slope of the given equation is $m =1/4$, and the y-intercept is $P (0,1)$

Plot the point (0,1) on the graph paper taking 0 on x-axis and 1 on y-axis.

Next using slope, plot the other point.

Slope can be read as rise and run to plot the graph.

So, slope is 1/4, therefore rise 1 that takes to 2 on y-axis and run 4 that takes 4 on x-axis, thus the respective coordinates are (4, 2)

If we extend the graph in $-x$ direction, that meets at (-4, 0)

Therefore, as shown in the diagram, the given equation represents a plane with a line passing through the coordinates (-4, 0), (0, 1) and (4, 2).

So, the correct answer is option 3.

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