How to Find Slope and Slope-intercept Form: The slope-intercept is a topic in algebra. Slope intercept form was employed in linear equations involving straight lines. It is a fairly straightforward topic in which we must determine the slope and y-intercept as well as draw a graph. The slope and y-intercept are easily found by anyone. The definition and examples of slope and slope-intercept form are covered in this post.
What is Slope?
The ratio of “vertical change” to “horizontal change” between (any) two unique points on a line is used to compute slope. The ratio is sometimes written as a quotient (“rise over run”), which gives the same number for every two different points on a single line.
The change in y coordinate with respect to the change in x coordinate of a line is known as its slope. It is denoted by m.
Δy is the net change in the y coordinate, while Δx is the net change in the x coordinate. As a result, they coordinate change in relation to the x coordinate change can be represented as,
m = rise/run = Δy/ Δx
This formula is also written as.
m = y2 – y1/x2 -x1
How to calculate Slope?
Let’s take some examples to calculate the slope by using a formula.
Example 1
Find the slope of the points (12, 15), (13, 16)?
Solution:
Step 1: Identify the values.
We know that equation can be written in general as
(x1, y1), (x2, y2)
Step 2: Compare the equation with the general equation and identify the values.
x1 = 12
x2 = 13
y1 = 15
y2 = 16
Step 3: Write the formula of slope.
m = y2 – y1/x2 -x1
Step 4: Put the values in the formula.
m = 16 – 15 / 13 – 12
m = 1/1
m = 1
The slope of points (12, 15), (13, 16) is 1.
Example 2
Find the slope of the points (19, -14), (11, -15)?
Solution:
Step 1: Identify the values.
We know that equation can be written in general as
(x1, y1), (x2, y2)
Step 2: Compare the equation with the general equation and identify the values.
x1 = 19
x2 = 11
y1 = -14
y2 = -15
Step 3: Write the formula of slope.
m = y2 – y1/x2 -x1
Step 4: Put the values in the formula.
m = -14 – (-15) / 11 – 19
m = -14 + 15 / 11 – 19
m = 1/-8
m = -1/8
The slope of points (19, -14), (11, -15) is -1/8.
This result can also be verified by Slope Calculator.
Example 3
Find the slope of the points (2, 4), (8, -5)?
Solution:
Step 1: Identify the values.
We know that equation can be written in general as
(x1, y1), (x2, y2)
Step 2: Compare the equation with the general equation and identify the values.
x1 = 2
x2 = 8
y1 = 4
y2 = -5
Step 3: Write the formula of a slope.
m = y2 – y1/x2 -x1
Step 4: Put the values in the formula.
m = -5 – 4 / 8 – 2
m = -9/6
m = -3/2
The slope of points (2, 4), (8, -5) is -3/2.
What is Slope-Intercept Form?
To obtain the equation of a line, use the slope-intercept form of a straight line. The slope of the line and the intercept cut by the line with the y-axis are required for the slope-intercept formula. Consider a straight line with the slope m and the y-intercept b.
The slope-intercept form equation for a straight line with a slope m, and b as the y-intercept is.
y = mx + b
How to Calculate Slope-Intercept Form?
Let’s take some examples to calculate the slope-intercept form by using the formula.
You can also use an online slope intercept form calculator to calculate the slope-intercept form.
Example 1
What is the equation of a line in slope-intercept form?
y = -5x + 3
Solution:
Step 1: Write the given equation.
y = -5x + 3
Step 2: write the formula of y-intercept form.
y = mx + b
Step 3: identify the values by comparing the given equation with the general formula.
Slope = m = -5
y intercept = b = 3
The line is decreasing from left to right due to a negative slope.
And passing at point (0, 3) through the y-axis.
Example 2
What is the slope-intercept form of a line passing through the points (21, -14) and (12, -15)?
Solution
Step 1: Identify the values.
We know that equation can be written in general as
(x1, y1), (x2, y2)
Step 2: Compare the equation with general equation and identify the values.
x1 = 21
x2 = 12
y1 = -14
y2 = -15
Step 3: Write the formula of slope.
m = y2 – y1/x2 -x1
Step 4: Put the values in the formula.
m = -14 – (-15) / 12 – 21
m = -14 + 15 / 12 – 21
m = 1/-9
m = -1/9
The slope of points (19, -14), (11, -15) is -1/9.
Step 5: write formula of y intercept form.
y = mx + b
Step 6: Put the value of slope in this formula.
y = -1/9x + b … (1)
Step 7: Put the point (12, -15) in the above equation.
y = -1/9x + b
-15 = -1/9(12) + b
-15 = -4/3 + b
b = -15 + 4/3
b = (-45 + 4)/3
b = -41/3
This is the y intercept.
Step 8: Put the value of b in equation (1).
y = -1/9x + (-41/3)
y = -1/9x – 41/3
Summary
The change in y coordinate with respect to the change in x coordinate of a line is known as its slope. It is denoted by m. having formula m = y2 – y1/x2 -x1
The slope has four types, positive slope, negative slope, zero slopes, and undefined slope. By using the formula, we can easily calculate the slope of given points. We use y = mx + b to find the slope-intercept form.