How to calculate slope-intercept form of a line with slope?
In algebra, the slope-intercept form is a general way to write the equation of the line. The slope-intercept form of the line cannot be written without using the slope of the line. The slope is the steepness or sharpness of the line. Both the concepts are essential for the calculation of the equation of the line accurately.
In this post, we will learn about the slope and the slope-intercept form along with a lot of examples.
How to Determine the Slope of the line?
The slope is widely used in algebra to measure the sharpness or steepness of the line. The slope is also used to measure the direction of the line. In general, the slope is moving in a line,from left to right in a line. The slope remains the same on each point of the line.
The slope is very important for the calculation of the equation of the line by using the slope-intercept form. The slope is a wide concept used in algebra and geometry. To determine a slope of the line, you can use an online tool such as a slope calculator which gives the accurate result of the slope problems in no time.
The slope is also calculated by using a formula.
m = y2 – y1 / x2 – x1
Example 1
Determine the slope of the line of the given points, (18, -5) and (19, 14)?
Solution
Step 1:Write names of the points from the given problem.
x1 = 18, x2 = 19, y1 = -5, y2 = 14
Step 2:Write the general equationto determine the slope.
m = (y2 – y1) / (x2 – x1)
Step 3:Place the values in the above equation.
m = (14 – (-5)) / (19 – 18)
m = (14 + 5) / (1)
m = 19/1
m = 19
Example 2
Determine the slope of the line of the given points, (-22, -5) and (12, 17)?
Solution
Step 1:Write names of the points from the given problem.
x1 = -22, x2 = 12, y1 = -5, y2 = 17
Step 2:Write the general equation to determine the slope.
m = (y2 – y1) / (x2 – x1)
Step 3:Place the values in the above equation.
m = (17 – (-5)) / (12 – (-22))
m = (17 + 5) / (22 + 12)
m = 22/34
m = 11/17
m = 0.6471
How to calculate the equation of the line by using the Slope-Intercept Form?
The slope-intercept form is one of the ways to calculate the equation of the line. The slope-intercept form can only be applicable to find the equation of the line when we have the slope of the line and y-intercept form of the equation.The slope-intercept form is very essential for such calculations. The process of finding the equation of the line by slope-intercept form takes place by the general equation of it.
y = mx + c
in the above equation, x and y are the fixed variables, m is the slope of the line, and c is the y-intercept form.
Example 1
Determine the equation of the line with the help of the slope-intercept form of the given points,(18, -5) and (19, 14)?
Solution
Step 1:Write names of the points from the given problem.
x1 = 18, x2 = 19, y1 = -5, y2 = 14
Step 2:Write the general equation to determine the slope.
m = (y2 – y1) / (x2 – x1)
Step 3:Place the values in the above equation.
m = (14 – (-5)) / (19 – 18)
m = (14 + 5) / (1)
m = 19/1
m = 19
Step 4:Now take the general equation to determine the slope-intercept form.
y = mx + c
Step 5:Determine the y-intercept form of the above equation by placing any given pair of points in the slope intercept form equation.
y = 19x + c
18 = 9(-5) + c
18 = -45 + c
c = 18+45
b = 63
Step 6:Put the calculated values in the formula.
y = mx + c
y = 19x +63
Hence, the required slope-intercept form of the given points is y = 19x + 63
You can use an online tool to find equation of line, y-intercept and slope intercept form by using a slope and y intercept calculator.
Example 2
Determine the equation of the line with the help of the slope-intercept form of the given points, (-22, -5) and (12, 17)?
Solution
Step 1:Write names of the points from the given problem.
x1 = -22, x2 = 12, y1 = -5, y2 = 17
Step 2:Write the general equation to determine the slope.
m = (y2 – y1) / (x2 – x1)
Step 3:Place the values in the above equation.
m = (17 – (-5)) / (12 – (-22))
m = (17 + 5) / (22 + 12)
m = 22/34
m = 11/17
m = 0.6471
Step 4:Now take the general equation to determine the slope-intercept form.
y = mx + c
Step 5:Determine the y-intercept form of the above equation by placing any given pair of points in the slope intercept form equation.
y = 11/17x + c
17 = 11/17(12) + c
17 = 132/17 + c
c = 17 – 132/17
c = 17 –7.7647
c = 9.2353
Step 6:Put the calculated values in the formula.
y = mx + c
y = 0.6471x – 9.2353
Hence, the required slope-intercept form of the given points is y = 0.6471x – 9.2353
Summary
In this post, we discussed the slope and the slope-intercept form. we also discussed how to calculate slope and slope intercept form and how they are helpful to determine the equation of the line. The slope is used in geometry and algebra to find the direction and measure the sharpness of the line.
The slope-intercept form is on the other hand, is an equation having fixed variables, slope, and the y-intercept form. For applying the slope intercept form equation, the slope is very important.