Question

Y = -x+5y=−x+5y=-x+55x+5y=205x+5y=205, x+5y=20)

AThe same line
B Distinct parallel lines
C Perpendicular lines
D Intersecting, but not perpendicular lines

Answer 1

Each equation, y = -3x, y = 0.2 + 0.74x, and y = -9.4 - 2x, meets the criteria for linear equations as they all represent straight lines with respective slopes and y-intercepts.

Step-by-step explanation:

The question asks which of the given equations represents linear equations. The characteristics of a linear equation are that it graphically represents a straight line, and it has a structure of the form y = mx + b, where 'm' is the slope and 'b' is the y-intercept.

• Option A, y = -3x, indicates a straight line with a negative slope, which is indeed linear.
• Option B, y = 0.2 + 0.74x, also details a straight line with a positive slope, thus qualifying as linear.
• Option C, y = -9.4 - 2x, shows another straight line with a negative slope, making it linear as well.

Therefore, all options (A, B, and C) represent linear equations. Considering the slope-intercept form described in Figure A1 on the Algebra of Straight Lines, Option A would have a slope of -3 and a y-intercept of 0, Option B would have a slope of 0.74 and a y-intercept of 0.2, and Option C would have a slope of -2 and a y-intercept of -9.4. These details clarify their linear nature.