Question

find an equation of the line graphed. write the equation in standard form. choose the correct equation below a. 4x + y = 3 b. x + 4y = 3 c. y = - 4x + 3 d. 4x + y - 3 = 0

Explanation:

Step1: Recall standard - form of a line

The standard form of a linear equation is $Ax + By=C$, where $A$, $B$, and $C$ are integers, and $A\geq0$. Option C is in slope - intercept form ($y = mx + b$), so we can eliminate it.

Step2: Check the $y$ - intercept

From the graph, the $y$ - intercept is $(0,3)$. Substitute $x = 0$ and $y=3$ into the remaining equations:

• For option A: $4(0)+3=3$, which is true.
• For option B: $0 + 4(3)=12

eq3$, so we can eliminate option B.

• For option D: $4(0)+3 - 3=0$, which is true.

Step3: Check the slope

The slope of the line can be found using two points. Let's use $(0,3)$ and $(1,-1)$. The slope $m=\frac{y_2 - y_1}{x_2 - x_1}=\frac{-1 - 3}{1-0}=-4$.
The slope - intercept form of the line is $y=-4x + 3$. Rearranging it to standard form gives $4x+y = 3$. Option D can be rewritten as $4x+y=3$ as well, but the standard form $Ax + By = C$ with $A\geq0$ is usually written without the $= 0$ on the right - hand side for this type of problem.

Answer:

A. $4x + y=3$