Question

what is the equation of the graphed line written in standard form?
○ ( x - 4y = 4 )
○ ( x + 4y = 4 )
○ ( y = \frac{1}{4}x - 1 )
○ ( y = -\frac{1}{4}x - 1 )
(graph with points (4, 0) and (0, -1) plotted)

Explanation:

Step1: Recall Standard Form

Standard form of a line is \(Ax + By = C\), so eliminate the slope - intercept form options (\(y=\frac{1}{4}x - 1\) and \(y =-\frac{1}{4}x-1\)) as they are in slope - intercept form (\(y = mx + b\)).

Step2: Test Points in Remaining Equations

We have two points on the line: \((0,-1)\) (the y - intercept) and \((4,0)\) (the x - intercept).

• For the equation \(x-4y = 4\):
• Substitute \(x = 0,y=-1\): \(0-4\times(-1)=0 + 4=4\), which satisfies the equation.
• Substitute \(x = 4,y = 0\): \(4-4\times0=4-0 = 4\), which satisfies the equation.
• For the equation \(x + 4y=4\):
• Substitute \(x = 0,y=-1\): \(0+4\times(-1)=0-4=-4

eq4\), so this equation does not satisfy the point \((0,-1)\).

Answer:

A. \(x - 4y = 4\)