Question

question 4 of 5
identify the graph of y = -x + 2.
graphs are shown, including a vertical line, a horizontal line, a line with positive slope, and a line with negative slope (the correct one for y = -x + 2)

Explanation:

Step1: Recall Linear Equation Form

A linear equation in slope - intercept form is $y = mx + b$, where $m$ is the slope and $b$ is the y - intercept. A linear equation with no solution when compared to another linear equation (presumably $y=0$ or a horizontal line, but more likely two parallel lines) or a non - linear situation? Wait, actually, if we consider the equation of a vertical line $x = a$ (which is not a function and has an undefined slope) and a horizontal line $y = b$ (slope 0), they are perpendicular. But for a linear equation (a function) $y=mx + b$, if we have a situation where it's a vertical line (not a function) or a line with an undefined slope, but the question is about which graph represents a linear equation with no solution? Wait, maybe the question is about a linear equation that has no solution when compared to another equation, but the graphs are of different types. Wait, a vertical line is not a function and has an undefined slope. A linear equation (function) has the form $y = mx + b$. A vertical line $x=a$ is not a function and can be thought of as a linear relation with no solution in the context of a function? Wait, maybe the first graph is a vertical line. Let's analyze the graphs:

• The first graph: Vertical line (parallel to y - axis), equation $x = a$. This is a linear relation but not a function (fails vertical line test for functions, but as a relation, it's linear). A linear equation in the form $x=a$ has an undefined slope.
• The second graph: Horizontal line (parallel to x - axis), equation $y = b$, slope 0, linear function.
• The third graph: A line with positive slope, $y=mx + b$, $m>0$, $b>0$, linear function.
• The fourth graph: Maybe a horizontal line? Wait, no, the fourth graph looks like x - axis? Wait, no, the fourth graph is x - axis? Wait, no, the fourth graph is a horizontal line (x - axis is $y = 0$).

Wait, the question is "Which graph represents a linear equation with no solution?" Wait, maybe the question is about a linear equation that has no solution when considered as a function? No, a linear equation (function) $y=mx + b$ always has solutions (for every x, there is a y, and for every y, if $m
eq0$, there is an x). A vertical line $x = a$ is a linear relation (not a function) and has the form $x=a$, which can be considered as a linear equation with an undefined slope. If the question is about a linear equation that is not a function (has no solution in the context of a function, since it fails the vertical line test for functions), then the vertical line (first graph) is the one.

Step2: Identify the Graph

The first graph is a vertical line (parallel to the y - axis). A linear equation in the form $x=a$ (vertical line) is a linear relation. If we consider a linear equation as a function, a vertical line is not a function (so has no solution in the function - sense, because for a function, each x has exactly one y, but for $x=a$, one x has infinitely many y's). So the first graph (the top - most graph, vertical line) represents a linear equation (relation) that has no solution when considered as a function.

Answer:

The top - most graph (the first graph)