Final answer:
To write an equation resulting in one solution given y=-2x+0.5, one could use a linear equation with a different slope, such as y=3x+1, ensuring the lines intersect at one point.
Step-by-step explanation:
The question from the student involves writing an equation that would result in one solution given the initial linear equation y=-2x+0.5. To create a new equation with exactly one solution, one could simply write another linear equation with a different slope. For example, y=3x+1 would intersect the original line at exactly one point, as the slopes (-2 for the first equation and 3 for the second equation) are not equal, ensuring the lines are not parallel and will cross at a single point.
The equations discussed are all linear, meaning they can be written in the form y = mx + b, where m is the slope and b is the y-intercept. According to Practice Test 4 Solutions 12.1 Linear Equations, the linear form is confirmed as all options A, B, and C are linear equations.
The solution to the student’s query also touches on key concepts of linear equations and the idea that any line on a graph with a constant slope is a linear representation of a function or an equation. A one-solution system implies the intersection of two non-parallel lines, which is also an essential concept in algebra.