Final answer:
The equation y = -x + 1 intersects the y-axis at the point (0, 1). It intersects the x-axis at the point (1, 0). Therefore, the correct answer is (a) The graph intersects the x-axis at (1, 0) and the y-axis at (0, 1).
Step-by-step explanation:
The equation given is y = -x + 1. When the equation of a line is written in the form y = mx + c, it's clear that m is the slope of the line and c is the y-intercept. In this case, the slope (m) is -1 (which means the line will be sloping downwards) and the y-intercept (c) is 1 (so the line crosses the y-axis at the point (0, 1)).
To find where the line intersects the x-axis, we set y to 0 and solve for x (because any point on the x-axis has a y-coordinate of 0). So, 0 = -x + 1 simplifies to x = 1. Therefore, the line intersects the x-axis at the point (1, 0). Therefore, the correct answer is (a) The graph intersects the x-axis at (1, 0) and the y-axis at (0, 1).
Learn more about Graphing Linear Equations