Question

Given the steps Y-(-2) = (x-3), y+2 = 4 -, y+2+2 = -2, y = ix-, and the point-slope form to write the equation of a line with a slope of 3/4 passing through the point (3,-2), determine if the student made an error.

Answer 1

The student made an error in their steps. The correct equation is y = (3/4)x - 17/4.

Step-by-step explanation:

The student made an error in their steps. The equation provided in step y = ix-, where i represents a constant, is not correct. In order to write the equation of a line with a slope of 3/4 passing through the point (3,-2) in point-slope form, we can use the formula y - y1 = m(x - x1), where (x1, y1) is the given point and m is the slope. Plugging in the values, we get y - (-2) = (3/4)(x - 3).

Expanding the equation, we get y + 2 = (3/4)x - 9/4. Simplifying further, we subtract 2 from both sides to isolate y, giving us y = (3/4)x - 17/4. This is the correct equation of a line with a slope of 3/4 passing through the point (3,-2).