Types of Slopes and Y-Intercept

Writing Equations in slope Intercept Form

y = mx +b

​Type 1 - Given a Slope and y - intercept.

y = m​x + b

Where m is the slope and b is the y-intercept.

• Simply replace the values for m and b into the equation.​

Multiple Choice

If m=3 and b=6, what is the correct slope intercept equation?

• y=3-6
• y=3x-6
• y=3x+6
• y=6x+3

Multiple Choice

Determine the slope and y-intercept.         y = 3/2x + 3

• slope: 5   y-intercept:  (0,3) 
• slope: 3/2   y-intercept:  (0,3) 
• slope:  4  y-intercept:  (0,3/2)
• slope: 1/5   y-intercept:  (0,5) 

Multiple Choice

How would you write the equation with a slope of 2/3 and a y-intercept of -3

• y=3/2x+3
• y=2/3-3
• y=2/3x-3
• y=2/3x+3

​Type 2 - Given a Point and the slope.

​

​Steps

Use the ordered pair to substitute the x and y values into the equation:

y = mx +b

Substitute the slope for m and solve for b.

Write the Equation.​

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Multiple Choice

Write the equation of the line passes through the point (3,-1) and has a slope of 2.

• y = 3x - 1

• y = 2x - 5

• y = 2x - 7

• y = -x + 3

Multiple Choice

Write the equation of the line passes through the point (2,1) and has a slope = 4.

• y = 3x - 2

• y = 4x - 7

• y = 4x + 7

• y = 3x + 3

​Type 3 - Given 2 points.

​Steps

1. Find the slope between the two points - replace this for m.

2. Use one of the two given points to find x and y

3. Solve for b.

4. Write the Equation.​

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Multiple Choice

In slope-intercept form, write the equation of the line passing through the points (-3,4) and (-4,2).

• y = -2x + 10

• y = -2x - 10

• y = 2x - 10

• y = 2x + 10

Multiple Choice

In slope-intercept form, write the equation of the line passing through the points (-4,1) and (-3,2).

• y = -x + 5

• y = x + 5

• y = x - 5

• y = -x + 5

​Writing Equations from a graph or a table.

​Steps

Determine m and b from the graph or table and write the equation

​OR

​Use the Desmos Calculator to determine m and b and write the equation.​

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Multiple Choice

Given the table, write the equation in the slope-intercept form.

• y = 1/3x + 6
• y = 3x + 6
• y = 2x + 6
• y = 1/2x + 6

Multiple Choice

Write the equation of the line.

• y = -1/3x - 2
• y = 1/3x - 2
• y = 3x - 2
• y = -3x - 2

Multiple Choice

What is the equation of this line?

• y = 2x +2
• y = 2x -2
• y = -x + 2
• Cannot be Determined