Determine the Slope and Y Intercept

Slope:

The slope is defined as the ratio of the "rise" divided by the "run" between two points on a line, or in other words, the ratio of the altitude change to the horizontal distance between any two points on the line. Given two points (x1,y1) and (x2,y2) on a line, the slope m of the line is




Y intercept:

In the coordinate system, the y intercept of a line is a point at which the line cuts the Y-axis. The y-intercept of a line is denoted as (0, y)




Example Problems to Determine the Slope and Y Intercept:

Example problem 1:

Determine the slope and y intercept of y = 7x - 12

Solution:

Step 1: Given equation

y = 7x - 12

Step 2: The slope intercept form of a line equation is given by

y = mx + b

Where,

m → slope

b → y intercept

Step 3: Compare the given equation with the slope intercept form

By comparing the given equation with the slope intercept form, we get

m = 7     and b = - 12

Step 4: Solution

Therefore,  Slope = 7

y intercept = - 12

Example problem 2:

Determine the slope and y intercept of 2x - 5y = 4

Solution:

Step 1: Given equation

2x - 5y = 4 ................... (1)

Step 2: Subtract 2x on both sides of the equation 2x - 5y = 4

2x - 5y - 2x  = 4 - 2x

- 5y = 4 - 2x

Step 3: Divide by (-5) on both sides of the equation

Therefore,

y = `2/5` x - `4/5`

y = 0.4x - 0.8 ............. (2)

Step 4: The slope intercept form of a line equation is given by

y = mx + b

Where,

m → slope

b → y intercept

Step 5: Compare the equation (2) with the slope intercept form of a line equation

By comparing the equation (2) with the slope intercept form, we get

m = 0.4     and b = - 0.8

Step 6: Solution

Therefore,  Slope = 0.4

y intercept = - 0.8

Example problem 3:

Determine the slope and y intercept of 9x + 3y = 0

Solution:

Step 1: Given equation

9x + 3y = 0 ............ (1)

Step 2: Subtract 9x on both sides of the equation 9x + 3y = 0

9x + 3y - 9x = - 9x

3y = - 9x

Step 3: Divide by 3 on both sides of the equation

Therefore,

y = - 3x ............... (2)

Step 2: The slope intercept form of a line equation is given by

y = mx + b

Where,

m → slope

b → y intercept

Step 3: Compare the equation (2) with the slope intercept form of a line equation

By comparing the equation (2) with the slope intercept form, we get

m = - 3     and b = 0

Step 4: Solution

Therefore,  Slope = - 3

y intercept = 0

Practice Problems to Determine the Slope and Y Intercept:

1) Determine the slope and y intercept of y = 4x - 13

2) Determine the slope and y intercept of 5x + y = 5

3) Determine the slope and y intercept of 3/2 + 2y = 4

Solutions:

1) Slope = 4; y intercept = - 13

2) Slope = - 5; y intercept = 5

3) Slope = -0.75; y intercept = 2