Question

which is true of the standard form of the equation of the line graphed? the value of a can be –1 if the value of c is 3 and the value of b is 0. the value of a can only be 1, the value of c can only be –3, and the value of b is 0. the standard form of the equation can be shown as 3x = –9. the standard form of the equation can only be x + 3 = 0.

Explanation:

Step1: Identify the line's equation

The graph shows a vertical line at \( x = -3 \). In standard form \( Ax + By = C \), for a vertical line \( By = 0 \) (so \( B = 0 \)), and \( Ax = C \). For \( x = -3 \), we can rewrite it as \( x + 3 = 0 \) (which is \( 1x + 0y = -3 \)) or \( -x - 3 = 0 \) (which is \( -1x + 0y = 3 \)), etc.

Step2: Analyze each option

• Option 1: If \( A = -1 \), \( B = 0 \), \( C = 3 \), the equation is \( -1x + 0y = 3 \), which simplifies to \( x = -3 \), matching the line. This is possible.
• Option 2: Claims \( A \) can only be 1, \( C \) only -3. But we saw \( A \) can be -1, \( C \) 3, so this is false.
• Option 3: \( 3x = -9 \) simplifies to \( x = -3 \), but standard form can have different coefficients (like \( x + 3 = 0 \) or \( -x - 3 = 0 \)), so it's not the only form.
• Option 4: Claims the only form is \( x + 3 = 0 \), but we can have equivalent forms (e.g., \( 2x + 6 = 0 \)), so this is false.

Answer:

The value of A can be -1 if the value of C is 3 and the value of B is 0.