Question

7)
y = 2x + 3
(table with x values -2, -1, 0, 1, 2 and corresponding y values -1, 1, 3, 5, 7; coordinate plane with some plotted points and a line sketch)

Explanation:

Step1: Verify the table with the equation

We have the linear equation \( y = 2x + 3 \). Let's check each \( x \)-value in the table:

• For \( x = -2 \): \( y = 2(-2)+3=-4 + 3=-1 \) (matches the table).
• For \( x=-1 \): \( y = 2(-1)+3=-2 + 3 = 1 \) (matches the table).
• For \( x = 0 \): \( y=2(0)+3 = 3 \) (matches the table).
• For \( x = 1 \): \( y=2(1)+3=2 + 3 = 5 \) (matches the table).
• For \( x = 2 \): \( y=2(2)+3=4 + 3 = 7 \) (matches the table).

Step2: Analyze the graph plotting

The equation \( y = 2x+3 \) is in slope - intercept form (\( y=mx + b \)) where the slope \( m = 2 \) and the \( y \)-intercept \( b = 3 \). The \( y \)-intercept is the point where \( x = 0 \), so the point \( (0,3) \) should be on the line. The slope of 2 means for every 1 unit increase in \( x \), \( y \) increases by 2 units. Looking at the plotted points, they seem to follow this pattern (e.g., from \( (0,3) \) to \( (1,5) \), \( x \) increases by 1, \( y \) increases by 2; from \( (1,5) \) to \( (2,7) \), same pattern, and for negative \( x \)-values, as \( x \) decreases by 1 (from \( 0\) to \( - 1\)), \( y \) decreases by 2 (from \( 3\) to \( 1\)) etc.). So the table is correctly filled and the graph (if we were to complete it) should be a straight line passing through these points with slope 2 and \( y \)-intercept 3.

Answer:

The table values are correct for the equation \( y = 2x + 3 \), and the plotted points follow the linear relationship defined by the equation.