Final answer:
The student's question involves labeling each of six given equations to understand the lines they represent on a graph. Each equation is categorized based on its form, whether it is a standard linear equation, vertical line, horizontal line, or a line with a specific slope and y-intercept.
Step-by-step explanation:
The student has asked to label each line with its correct equation. Linear equations can be represented in the form y = mx + b, where m is the slope of the line and b is the y-intercept. Using this standard form, we can identify each given equation:
- x + 5y = 10 is a linear equation in standard form.
- x + y = -9 is another linear equation where both x and y are on the same side of the equation.
- x = -5 is a vertical line where all points on the line have an x-coordinate of -5.
- y = -5 is a horizontal line where all points on the line have a y-coordinate of -5.
- y = 2x + 7 is in slope-intercept form with a slope of 2 and a y-intercept of 7.
- y = x represents a line where the slope is 1, indicating that for every increase in x, y increases by the same amount.
When graphing these equations, each one will produce a straight line except for the vertical and horizontal lines which are represented by their respective constant x or y values. If needed, the student can also create tables of values or graph the equations to better visualize the lines and their slopes.