Answer:
y = -x + 8
Explanation:
Let's break down the equation step by step to understand it better.
The equation in point-slope form is given as:
y - y1 = m(x - x1)
In this case, we have:
y - 0 = -1(x - 8)
The point-slope form uses a specific point (x1, y1) on the line and the slope (m) of the line.
Here, the point (x1, y1) is (8, 0), which represents a point on the line. This means that when x = 8, y = 0. The graph has a point at (8, 0), which confirms this information.
The slope (m) is -1 in this equation. The slope represents the rate at which y changes with respect to x. In this case, since the slope is -1, it means that for every unit increase in x, y decreases by 1. The negative sign indicates that the line has a downward slope.
By substituting the values into the equation, we get:
y - 0 = -1(x - 8)
Simplifying further:
y = -x + 8
This is the final equation of the line in slope-intercept form. It tells us that y is equal to -x plus 8. In other words, the line decreases by 1 unit in the y-direction for every 1 unit increase in the x-direction, and it intersects the y-axis at the point (0, 8).
If the graph has points at (0, 8) and (8, 0), the equation y = -x + 8 accurately represents that line.