Question

Which of the following equations describes all points on a horizontal line that passes through the point (-3, 7)?

a) y = 7
b) x = -3
c) y = -3x + 7
d) y = 7x - 3

Answer 1

The correct equation for a horizontal line passing through the point (-3, 7) is y = 7, as it represents a line where all points have a y-value of 7, confirming a horizontal orientation without any slope.

Step-by-step explanation:

The question concerns identifying which equation represents a horizontal line that goes through a certain point. A horizontal line has a slope of 0, meaning there is no change in the y-value as the x-value changes. Therefore, the equation for a horizontal line would not have an x variable present, but instead have a constant y-value across all points.

Given the options, the correct equation that represents a horizontal line passing through the point (-3, 7) is y = 7. This is because every point on this line will have a y-value of 7 regardless of the x-value. The other options include x or both x and y variables, which would imply a slope, making those lines not horizontal. Specifically, option a would be a straight line with negative slope. Option b has a vertical line, which is not the same as a horizontal line. Option c also indicates a straight line with negative slope. Option d indicates a straight line with positive slope.