All the x-values will be And so if we were to plot this. Equation of a Line slope and intercept form Definition: When the x and the y variable change in opposite directions, the slope will be negative.
In this form, m is the slope and b is the y-intercept. One thing that some students have trouble with is the notation in the formula. This type of linear equation was shown in Tutorial And when you write something in slop-intercept form, where you explicitly solve for y, y is equal to some constant times x to the first power plus some other constant, the second one is going to be your intercept, your y-intercept, or it's going to be a way to figure out the y-intercept, the intercept itself is this point, the point at which the line intercepts the y axis, and then this two is going to represent your slope.
As you reduce it below zero, the negative slope makes the line slope down to the right. When you are first doing these computations, it may be helpful to write everything out to avoid confusion. Graphing a Positive Slope Start with the point 0, So one way to think about it, the reason why this is called slope-intercept form is it's very easy to calculate the y-intercept.
Since the rise is positive 2, I counted up 2. Yes, it is rising; therefore, your slope should be positive. Since the slope is positive, the line slopes up and to the right. Try it yourself Press "reset", then "hide details" Adjust the sliders until you see a line that appeals to you Estimate the slope and y-intercept of the line and write down the equation for the line Click on "show details" and see how close you got Hints The point where the line crosses the vertical y-axis is the y-intercept - b For each increase of one on the horizontal x-axis, how much does the line go up or down.
What is the slope of the line connecting the points 6, 9 and -2, 1. Think back to the original points of -1, 3 and 4, The equation and the line will change accordingly. If the slope is negative you can plot your next point by going down and right OR up and left. However, when you begin using the slope formula discussed in the next section, it can become confusing to have too many formulas for slope.
Our line is going to look like, is going to look, is going to look something like, is going to look, let me see if I can, I didn't draw it completely at scale, but it's going to look something like this. Site Navigation Investigating Slopes of Lines Often when a student hears the word slope, many different things come to mind.
By using we would get Are There Special Cases. This graph has a positive slope. So we substitute zero into the equation for y, and solve it for x:.
The m variable is the slope of the line and controls its 'steepness'. A positive value has the slope going up to the right. A negative slope goes down to the right. The b variable is the y intercept - the point where the line crosses the y axis.
Adjust the sliders above to vary the values of a and b, and note the effects they have on the graph. Another form. Writing Algebra Equations Finding the Equation of a Line Given Two Points.
We have written the equation of a line in slope intercept form and standard form. We have also written the equation of a line when given slope and a point.
Now we are going to take it one step further and write the equation of a line when we are only given two points that are on that line. Steps for Graphing a Line With a Given Slope. Plot a point on the y-axis. (In the next lesson, Graphing with Slope Intercept Form, you will learn the exact point that needs to be plotted first.
For right now, we are only focusing on slope.) Look at the numerator of the slope. Steps for Graphing a Line With a Given Slope. Plot a point on the y-axis.
(In the next lesson, Graphing with Slope Intercept Form, you will learn the exact point that needs to be plotted first. For right now, we are only focusing on slope.) Look at the numerator of the slope. This is called the slope-intercept form because "m" is the slope and "b" gives the y-intercept.
(For a review of how this equation is used for graphing, look at slope and graphing.). I. This is called the slope-intercept form because "m" is the slope and "b" gives the y-intercept.
(For a review of how this equation is used for graphing, look at slope and graphing.). I like slope-intercept form.How to write a line in slope intercept form