Question

which graph matches the equation ( y + 3 = 2(x + 3) )?

Explanation:

Step1: Simplify the equation

Start with the given equation \( y + 3 = 2(x + 3) \). Distribute the 2 on the right side: \( y + 3 = 2x + 6 \). Then, subtract 3 from both sides to solve for \( y \): \( y = 2x + 6 - 3 \), so \( y = 2x + 3 \).

Step2: Identify key points

Y - intercept:

The y - intercept occurs when \( x = 0 \). Substitute \( x = 0 \) into \( y = 2x + 3 \). Then \( y=2(0)+3 = 3 \). So the y - intercept is \( (0, 3) \).

X - intercept:

The x - intercept occurs when \( y = 0 \). Substitute \( y = 0 \) into \( y = 2x + 3 \). We get \( 0=2x + 3 \). Subtract 3 from both sides: \( - 3=2x \). Then divide both sides by 2: \( x=-\frac{3}{2}=- 1.5 \). But we can also check the point - slope form. The original equation \( y + 3 = 2(x + 3) \) is in point - slope form \( y - y_1=m(x - x_1) \), where the point \( (x_1,y_1)=(-3,-3) \) (since \( y - (-3)=2(x - (-3)) \) which is \( y + 3 = 2(x + 3) \)).

Now, check the two graphs:

• The first graph has a y - intercept at \( (0,3) \) and passes through \( (-3,-3) \). Let's verify if \( (-3,-3) \) satisfies the equation \( y + 3 = 2(x + 3) \). Substitute \( x=-3 \) and \( y = - 3 \): Left side: \( -3 + 3=0 \), Right side: \( 2(-3 + 3)=2(0)=0 \). It satisfies. Also, when \( x = 0 \), \( y=3 \), which matches the y - intercept.

• The second graph has a y - intercept at \( (0,6) \) and x - intercept at \( (-3,0) \). Let's check if \( (0,6) \) satisfies \( y = 2x+3 \). Substitute \( x = 0 \), \( y=2(0)+3 = 3

eq6 \). So it does not satisfy the equation.

Answer:

The graph with the y - intercept at \( (0, 3) \) and passing through \( (-3,-3) \) (the upper - left graph among the two shown)