Question

Determine which form of a line the given equation is in. Then, determine the slope and y-intercept.

y - 4 = 7(2-3)
a It is in point-slope form; the slope is m = 7, and the y-intercept is (0, – 17).
b It is in standard form; the slope is m = 7, and the y-intercept is (0, – 17).
c It is in slope-intercept form; the slope is m = 7, and the y-intercept is (0, – 3)
d It is in point-slope form; the slope is m = 7, and the y-intercept is (0, – 4).

Answer 1

The equation represents a horizontal line with a slope of 0 and a y-intercept of (0, -3), not point-slope form with a slope of 7 as initially suggested.

The correct answer is C.

Step-by-step explanation:

The given equation y - 4 = 7(2-3) is initially in point-slope form. The equation can be simplified by performing the multiplication inside the parentheses, giving us y - 4 = 7(2) - 7(3), which simplifies to y - 4 = 14 - 21. Simplifying further, we get y - 4 = -7. Adding 4 to both sides yields y = -7 + 4, which simplifies to y = -3. This reveals that the line is actually horizontal and has no slope, which implies that the initial analysis of m = 7 was incorrect, and there is a misunderstanding because the point-slope form should include a variable x in the equation. A horizontal line like y = -3 has a slope of 0 and a y-intercept of (0, -3).

Therefore, the correct response to the given problem would be:

• It is in horizontal line form.
• The slope is m = 0.
• The y-intercept is (0, -3).