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How To Find Slope And Slope-intercept Form By Using Formulas?

How To Find Slope And Slope-intercept Form By Using Formulas?

How To Find Slope And Slope-intercept Form By Using Formulas?

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.

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