Going to the right of the origin are the positive values, and going to the left of the origin are the negative values. If the slope is positive, then the rise and the run need to either be BOTH positive or BOTH negative. In other words, you will be going up and to the right OR down and to the left.
The slope formula is sometimes called "rise over run." The simple way to think of the formula is: M=rise/run. M stands for slope. Your goal is to find the change in the height of the line over the horizontal distance of the line.
The Slope of a Line. Slopes can be whole numbers or fractions and either positive or negative. All slopes can be converted to a fraction form that tells you how much the line changes in the y direction over how much the line changes in the x direction. This is easy to remember as the phrase 'rise over run.
Terms in this set (8)
- Slope. y2 - y1 / x2 - x1 = slope.
- Slope Intercept form. y = mx + b.
- Point slope form. y - y1 = m ( x - x1)
- Standard Form. Ax + By = C.
- x - axis. The horizontal line on a graph.
- y - axis. The vertical line on a graph.
- X - intercept. The point on a line that intercepts on the x axis.
- Y - intercept.
To find the y intercept using the equation of the line, plug in 0 for the x variable and solve for y. If the equation is written in the slope-intercept form, plug in the slope and the x and y coordinates for a point on the line to solve for y.
In mathematics, the slope or gradient of a line is a number that describes both the direction and the steepness of the line. A slope with a greater absolute value indicates a steeper line. The direction of a line is either increasing, decreasing, horizontal or vertical.
To graph a linear equation, we can use the slope and y-intercept.
- Locate the y-intercept on the graph and plot the point.
- From this point, use the slope to find a second point and plot it.
- Draw the line that connects the two points.
Convert rise and run to the same units of measure, then divide the rise by the run to find the decimal form. Finally, get the inverse tangent of the decimal to find the angle in degrees. Rise is equal to the height of a line and run is equal to the horizontal length of a line.
The slope of a line characterizes the direction of a line. To find the slope, you divide the difference of the y-coordinates of 2 points on a line by the difference of the x-coordinates of those same 2 points .
To write an equation in slope-intercept form, given a graph of that equation, pick two points on the line and use them to find the slope. This is the value of m in the equation. Next, find the coordinates of the y-intercept--this should be of the form (0, b). The y- coordinate is the value of b in the equation.
In the equation of a straight line (when the equation is written as "y = mx + b"), the slope is the number "m" that is multiplied on the x, and "b" is the y-intercept (that is, the point where the line crosses the vertical y-axis). This useful form of the line equation is sensibly named the "slope-intercept form".
The equation of any straight line, called a linear equation, can be written as: y = mx + b, where m is the slope of the line and b is the y-intercept. The y-intercept of this line is the value of y at the point where the line crosses the y axis.
Equation of a Straight Line. Equations of straight lines are in the form y = mx + c (m and c are numbers). m is the gradient of the line and c is the y-intercept (where the graph crosses the y-axis).
The "slope" of a vertical line. A vertical line has undefined slope because all points on the line have the same x-coordinate. As a result the formula used for slope has a denominator of 0, which makes the slope undefined..
Multiply the slope by the run to calculate the rise between subsequent points. In the example, if you wanted to know the rise given a run of 10, multiply 10 times 0.6 to calculate a rise of 6. Divide the rise by the slope to calculate the run.
Lesson Summary
' 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. It will look like 'y = something.The -axis consists of all the points in the -plane which satisfy . So, if the -intercept is zero that means that the -value of the place where the function crosses the -axis is . That means that where the function crosses the -axis, meaning the place where the -value is , that the height above the -axis is also zero.
If the denominator of the fraction is 0, the slope is undefined. This occurs if the x value is the same for both points. The graph would be a vertical line and would indicate that the x value stays constant for every value of y. If the numerator of the fraction is 0, the slope is 0.
The equation of a line is typically written as y=mx+b where m is the slope and b is the y-intercept. If you know two points that a line passes through, this page will show you how to find the equation of the line. Fill in one of the points that the line passes through
Two points also determine a ray, a segment, and a distance, symbolized for points A and B by AB (or BA when B is the endpoint), AB, and AB respectively.
Slope of a horizontal line. When two points have the same y-value, it means they lie on a horizontal line. The slope of such a line is 0, and you will also find this by using the slope formula.
To graph the equation of a line written in slope-intercept (y=mx+b) form, start by plotting the y-intercept, which is the b value. The y-intercept is where the line will cross the y-axis, so count up or down on the y-axis the number of units indicated by the b value.
The slope of a line measures the steepness of the line. Most of you are probably familiar with associating slope with "rise over run". Rise means how many units you move up or down from point to point. Run means how far left or right you move from point to point. On the graph, that would mean a change of x values.
See what you get.) The formula for slope is sometimes referred to as "rise over run", because the fraction onsists of the "rise" (being the change in y, going up or down) divided by the "run" (being the change in x, going from left to the right).
Steps
- Take the coordinates of two points you want to find the distance between. Call one point Point 1 (x1,y1) and make the other Point 2 (x2,y2).
- Know the distance formula.
- Find the horizontal and vertical distance between the points.
- Square both values.
- Add the squared values together.
- Take the square root of the equation.
