Which of the following is the graph of the function y=x+2? (1 point) Responses Image with alt text: An illustration shows a coordinate plane with four quadrants. The x-axis and y-axis both range from negative 4 to 4 in one unit increments. A downward slanting line is graphed on the coordinate plane. The line passes through points plotted at left parenthesis 0 comma 2 right parenthesis and left parenthesis 2 comma 0 right parenthesis. Image with alt text: An illustration shows a coordinate plane with four quadrants. The x-axis and y-axis both range from negative 5 to 5 in one unit increments. A parabola opening upward is graphed on the coordinate plane. The parabola is formed by connecting points plotted at left parenthesis negative 4 comma 2 right parenthesis, left parenthesis negative 2 comma 0 right parenthesis, and left parenthesis 0 comma 2 right parenthesis. Image with alt text: An illustration shows a coordinate plane with four quadrants. The x-axis and y-axis both range from negative 4 to 4 in one unit increments. An upward slanting line is graphed on the coordinate plane. The line passes through points plotted at left parenthesis negative 2 comma 0 right parenthesis, and left parenthesis 0 comma 2 right parenthesis. Image with alt text: An illustration shows a coordinate plane with four quadrants. The x-axis and y-axis both range from negative 4 to 4 in one unit increments. A circle is graphed on the coordinate plane. The circle is formed by connecting points plotted at left parenthesis negative 2 comma 0 right parenthesis, left parenthesis 0 comma 2 right parenthesis, and left parenthesis 2 comma 0 right parenthesis. Skip to navigation

Question

GPT-4o mini · Answer

The function $ y = x + 2 $ is a linear function, which can be rewritten in slope-intercept form $ y = mx + b $ where $ m $ is the slope and $ b $ is the y-intercept. In this case, the slope $ m = 1 $ and the y-intercept $ b = 2 $. This line will pass through the point where $ x = 0 $ (which gives $ y = 2 $), so one point on the line is $ (0, 2) $. Additionally, if $ x = -2 $, then $ y = -2 + 2 = 0 $, giving us another point $ (-2, 0) $. To determine which graph correctly represents this function, we need to find a straight line that: 1. Passes through the points $ (0, 2) $ and $ (-2, 0) $. 2. Has a positive slope, moving upwards to the right. Among the provided options, the graph that features a straight line passing through these points is the graph that shows an upward slanting line through the points $ (-2, 0) $ and $ (0, 2) $. Thus, the correct choice is the image showing the upward slanting line passing through the points $ (-2, 0) $ and $ (0, 2) $.