Point-Slope Form

point-slope form

Point Slope Form

Unit 5 section 3

Point-slope form is:

Example 1 Write the equation for a line with a slope of 3 that passses through the point (4,5).

Example 2 Write the equation of a line that passes through the points: (1,2) and (-2,-6)

Example 3 Rewrite the equation in slope-intercept form. y - 5 = -2(x + 3)

• Distribute m.
• Add/Subtract y1 to each side.

• Find m.
• Choose one point.

• Given m.
• Given point.

• m is the slope of the line
• (x1, y1) is a point on the line.

Identify

Recall

Substitute

Point-slope form is:

Example 1 Write the equation for a line with a slope of 3 that passses through the point (4,5).

y-y1 = m(x-x1)

• m = 3
• (4, 5) is a point on the line.

• Given m.
• Given point.

• m is the slope of the line
• (x1, y1) is a point on the line.

• m = 3
• (4, 5) is a point on the line.

y-5 = 3(x-4)

Identify

Recall

Substitute

Point-slope form is:

y-y1 = m(x-x1)

Example 2 Write the equation of a line that passes through the points: (1,2) and (-2,-6)

• m = 8

3

• (1, 2) is a point on the line.

• Given m.
• Given point.

• m = y2 -y1 = -6 - 2 = 8

x2 - x1 -2 - 1 3

• (1, 2) is a point on the line.

• m is the slope of the line
• (x1, y1) is a point on the line.

y-2 = 8 (x-1) 3

Identify

Recall

Simplify

Point-slope form is:

y-y1 = m(x-x1)

Example 3 Rewrite the equation in slope-intercept form. y - 5 = -2(x + 3)

y - 5 = -2(x + 3)

y - 5 = -2x + -6

Slope intercept form is:

y = mx + b

• Given m.
• Given point.

y - 5 = -2x - 6 + 5 + 5

• Distribute the m

• Add/Subtract y1 to both sides

• m is the slope of the line
• (x1, y1) is a point on the line.
• b is the y-intercept

y = -2x-1