The slope of a line is defined as the change in y-values divided by the change in x-values. This number measures how steep a line is. The slope of a line does not uniquely define it, but it does give us a lot of information. It is also a necessary ingredient in a line’s equation.

The steepness of a hill is called a slope. The slope is defined as the ratio of the vertical change between two points, the rise, to the horizontal change between the same two points, the run.

You can describe the slope, or steepness, of the ramp and stairs by considering horizontal and vertical movement along them. In conversation, you use words like “gradual” or “steep” to describe slope. Along a gradual slope, most of the movement is horizontal. Along a steep slope, the vertical movement is greater.

A negative slope means that two variables are negatively related; that is, when x increases, y decreases, and when x decreases, y increases. Graphically, a negative slope means that as the line on the line graph moves from left to right, the line falls.

Horizontal lines have no vertical change — it continues straight left or right. In other words, the change in the y values between any points on the graph is 0, since there is no change. This means that the slope of a horizontal line is 0 (m=0).

The slope of a line can be positive, negative, zero, or undefined. A horizontal line has slope zero since it does not rise vertically (i.e. y1 − y2 = 0), while a vertical line has undefined slope since it does not run horizontally (i.e. x1 − x2 = 0). because division by zero is an undefined operation.

Because a slope of 07 is 0 this is the slope of a horizontal line. The line perpendicular to this would be a vertical line. A vertical line, by definition, has an undefined slope.

04=0 is defined. 40 is not.

When the 0 is on the “top” of the fraction, that would mean that the two y-values are the same. Thus that line is horizontal (slope of 0). If the “bottom” of the fraction is 0 that means the two x-values are the same. Thus that line is vertical (undefined slope).

If an equation of a line in slope-intercept form (y=mx+b) has no x variable, this means that the slope is 0. Any number being multiplied by 0 equals 0. When m=0, this means that the “mx” portion of the line’s equation is 0. The result is that y=b.

The answer to this question is that there is no answer. By this we simply mean that there is no number which, when multiplied by 0, gives you 9. Mathematicians say that “division by 0 is undefined”, meaning there is no way to define an answer to the question in any reasonable or consistent manner.

0 divided by 3 is 0.

horizontal line

That means the change in x, which is the denominator of the slope formula, would be 5 – 5 = 0. Well you know that having a 0 in the denominator is a big no, no. This means the slope is undefined. As shown above, whenever you have a vertical line your slope is undefined.

A zero slope means there is no change in the y -coordinates as the x -coordinates change, so this is a horizontal line.

The slope of a line can be thought of as ‘rise over run. ‘ When the ‘rise’ is zero, then the line is horizontal, or flat, and the slope of the line is zero. Put simply, a zero slope is perfectly flat in the horizontal direction. The equation of a line with zero slope will not have an x in it.

As mentioned earlier slope is represented by the letter (m) and if you plug in one of your data points for x and y, use the number 4 as b, and the slope we just calculated, you will see that both sides of the equation are equal.

3 Answers. The slope is -1.

Two lines are parallel if the have the same slope. Example 1: Find the slope of the line parallel to the line 4x – 5y = 12. To find the slope of this line we need to get the line into slope-intercept form (y = mx + b), which means we need to solve for y: The slope of the line 4x – 5y = 12 is m = 4/5.

If two lines are cut by a transversal and the alternate exterior angles are equal, then the two lines are parallel. Angles can be equal or congruent; you can replace the word “equal” in both theorems with “congruent” without affecting the theorem. So if ∠B and ∠L are equal (or congruent), the lines are parallel.

Ways to Prove Two Lines Parallel

• Show that corresponding angles are equal.
• Show that alternative interior angles are equal.
• Show that consecutive interior angles are supplementary.
• Show that consecutive exterior angles are supplementary.
• In a plane, show that the lines are perpendicular to the same line.