Writing the equation of a line given slope and a point

Writing the equation of a line given slope and a point

Aim: How do you write the equation of a line in slope-intercept form using a point and the slope?

Open Ended

What is the equation of the graph shown here?

Open Ended

What is the equation of this graph?

Open Ended

Write the equation for this graph.

Example 1: Find the equation of the line that goes through point (3, 8) whose slope is 2/3.  

• 1. Use the equation y = mx + b and replace all the information to find b (y-intercept)

• y = mx + b ==> For point (3, 8); x = 3 and y = 8

• 8 = 2/3(3) + b  ==> 8 =  2 + b

•                                 -2    -2 

•                                  6 = b

• 2. Write the equation: y = 2/3x + 6

Example 2: Find the equation of the line that passes through point (4, -6) whose slope is -3/4.

• 1. Use the equation y = mx + b and replace all the information to find b (y-intercept).

• y = mx + b ==> From point (4, -6); x = 4 and y = -6

• -6 = -3/4(4) + b ==> -6 = -3 + b

• Add 3 to both sides: +3 +3

• b = -3

• 2. Write the equation: y = -3/4x - 3

Multiple Choice

Write the equation of the line whose slope is 2 and passes through (1, 4)

• y = 2x - 2

• y = 2x + 2

• y = 2x - 7

• y = 2x + 6

Multiple Choice

Write the equation of the line that passes through (-3, 5) and whose slope is 1/3.

• y = 1/3x - 6

• y = 1/3x - 5

• y = 1/3x + 5

• y = 1/3x + 6

Summary

To write the equation of a line when given a point and the slope, just replace into the equation y = mx + b.

• m will be the given slope.

•To find b (the y-intercept), just replace into the equation y = mx + b. X will be the first coordinate of the given point and y will be the second coordinate of the given point.