Geometry Parallel lines

Question

The equations of four lines are given. Identify which lines are parallel.

Line 1: y = -3/4 - 6

Line 2: y - 7 = -4 (x+9)

Line 3: y = -2x +6

Line 4: x + 4/3y = -5

Answer 1

Assuming line 1 equation is y = -3/4x -6. The equation is in y=mx+b form, where m is the slope, so the slope of that line is -3/4

This equation is in point-intercept form y-y1 = m(x - x1), where m is the slope, The slope of line 2 equation is -4

This equation is also in y=mx+b form, so the slope of line three equation is -2

This equation is in general ax + by = c form, where the slope is -a/b. The slope of line 4 equation is -3/4

Lines are parallel if their slopes are equal, so lines 1 and 4 are parallel.