the vertical axis on a coordinate plane is called the ____.
the measure of the steepness of a line is called its ____.
a system of equations with no solutions is described as ____.
a system of equations with at least one solution is described as ____.
if two lines have the same slope and different y-intercepts, they are ____.
the process of plotting a line by using the slope and y-intercept is known as solving by ____.

Question

Accepted Answer

### 1. The vertical axis on a coordinate plane is called the
# Brief Explanations:
In a coordinate plane (like the Cartesian plane), the vertical axis is defined as the y - axis. This is a fundamental concept in coordinate geometry (a subfield of Mathematics), where the coordinate plane has two axes: horizontal (x - axis) and vertical (y - axis) to locate points.
# Answer:
y - axis

### 2. The measure of the steepness of a line is called its
# Brief Explanations:
In the study of lines in coordinate geometry (or algebra when dealing with linear equations), the steepness of a line is quantified by a value called the slope. The slope can be calculated as the ratio of the change in y (rise) to the change in x (run) between two points on the line, i.e., $m=\frac{y_2 - y_1}{x_2 - x_1}$.
# Answer:
slope

### 3. A system of equations with no solutions is described as
# Brief Explanations:
For a system of linear equations (e.g., in the form of $a_1x + b_1y = c_1$ and $a_2x + b_2y = c_2$), if the lines represented by the equations are parallel (they never intersect), then there are no common solutions. Such a system is called inconsistent. In contrast, a consistent system has at least one solution.
# Answer:
inconsistent

### 4. A system of equations with at least one solution is described as
# Brief Explanations:
In the context of systems of equations (linear or otherwise), a system that has one or more solutions (i.e., there exists at least one set of values for the variables that satisfies all equations in the system) is termed a consistent system. This is the opposite of an inconsistent system (which has no solutions).
# Answer:
consistent

### 5. If two lines have the same slope and different y - intercepts, they are
# Brief Explanations:
In the slope - intercept form of a line $y = mx + b$ (where $m$ is the slope and $b$ is the y - intercept), if two lines have the same $m$ (slope) but different $b$ (y - intercept), they will never intersect. By the definition of parallel lines (lines in a plane that do not meet), such lines are parallel. If they had the same slope and same y - intercept, they would be coincident (the same line).
# Answer:
parallel

### 6. The process of plotting a line by using the slope and y - intercept is known as solving by
# Brief Explanations:
The slope - intercept form of a line is $y=mx + b$, where $m$ is the slope and $b$ is the y - intercept. To graph a line using this form, we first plot the y - intercept (the point $(0,b)$) and then use the slope (rise over run) to find another point on the line and draw the line through these points. This method is called the slope - intercept method (or solving by slope - intercept form).
# Answer:
slope - intercept (form)

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Question

Explanation:

1. The vertical axis on a coordinate plane is called the

Answer:

2. The measure of the steepness of a line is called its