When it comes to writing the equation of a straight line, we will find that there are two conventional methods of writing it. The one is known as point-slope form, and it requires the coordinates of one point and the slope of the line. The other way of writing the equation is slope-intercept form, which requires the slope of a line and y-intercept coordinates. If you form a point-slope form for a straight line, you need to do a bit of algebraic manipulation to rewrite the equation in slope-intercept form. It might become confusing sometimes because of its complicated calculations. So you can use a slope intercept form calculator to determine the equation by using the one slope, point, and intercept of the line.
Table of Contents
Recapping the Point Slope Form:
Before moving towards the point-slope form conversion to slope-intercept form, you need to understand how the point-form looks. So here is a recap of the point-slope form.
y -y1 = m (x – x1)
Here the variable “m” represents the slope of the straight line while x1 & y1 are the coordinates of that line, and they are said to be the x and y coordinates. You will see a line at the point-slope form along with its coordinates when the slope is filled in. then, it may look like this:
y+5=3(x−2)
The thing you need to know is, y + 5 from the left of the equation is equivalent to y – ( -5). In case it helps you to recognize the equation as a straight line, then you can write the same equation like this:
y−(−5)=3(x−2)
Do you want to convert this point-slope form equation for a straight line in the slope-intercept form? You can do that by using the manual procedure for it. Instead of the manual way, you can try using the slope intercept calculator to convert the equation in slope-intercept form from the point-slope form. The benefit of using this slope intercept form calculator is that it generates the results free of cost. So you don’t have to spend money on useless tools.
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Recapping Slope-Intercept Form:
Now, it’s time to have a quick recap about the slope-intercept form, which looks like:
y=mx+b
Just like the point-slope intercept form, in slope-intercept form “m” represents the straight-line slope. Here the variable “b” represents the y-intercept of the line and the x-coordinates of the point where a line crosses the y-axis. Below is an example of writing the equation into slope-intercept form.
y=5x+8
For the conversion of point-slope form into the slope-intercept form, the most simple way is to use the slope intercept form calculator that allows you to calculate the x and y-intercepts of the slope of a line by using the equation if slope intercept.
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How to Find Slope Intercept Form:
At the time of comparing both the ways of writing the equation of a line, you will notice that there are a few similarities. Both ways retain the y variable and x variable with the line slope. So, all you need here is to get the slope-intercept form from the point-slope form by doing a little bit of manipulation. Consider the below-mentioned example to understand it more clearly:
y+5=3(x−2)
The first step for converting the point-slope form to slope-intercept form is to use the distributive property to simplify the right side of the equation. After applying the distributive property, the equation looks like this:
y+5=3x−6
Now, subtract the 5 from both sides of the equation for isolating the “y” variable that provides the equation in point-slope form. I know this might be too confusing for you, especially when you are not good at calculations. Simply consider using the slope intercept form equation calculation that converts the point-slope form equation into slope intercept in fractions of seconds. You can use this free slope intercept form calculator without hassle to do the calculations.
