Slope Intercept Form

Given a point and slope

Given two points

Ex: Find an equation of the line with slope = -3 that contains the

point (4, 2) Start with the slope-intercept form of a linear equation y = mx + b

Slope = - 3 y = - 3x + b What is b, though?What is b, though?

Use the given point (4, 2) x = 4 and y = 2

y = - 3x + b 2 = - 3(4) + b

2 = -12 + b

14 = b

put it together

we have m and b

y = - 3 x + 14

Write an equation of a line that passes through (2, –3)

with slope

Step 1 The line has slope To find the y-intercept,

replace m with and (x, y) with (2, –3) in the

slope-intercept form. Then, solve for b.

Write an Equation Given Slope and One Point

Slope-intercept form

Replace m with ,y with –3,and x with 2.

Multiply.

Subtract 1 from each side.

Simplify.

Write an Equation Given Slope and One Point

Step 2 Write the slope-intercept form using

Slope-intercept form

Replace m with and b with –4.

Answer: The equation is

Write an Equation Given Slope and One Point

You can check your results using a graphing calculator!Online Graphing Calculator

Write an equation of a line that passes through (1, 4) and has a slope of –3.

Answer:

Write an Equation Given Slope and One Point

You can check your results using a graphing calculator!Online Graphing Calculator

Ex: Find an equation of the line containing the points (-2, 1) and (3, 5)

First, find the slope of the line containing the points:

Slope = m = rise = y1 - y2 = 1 – (5)

run x1 - x2 -2 – 3

Point 1 Point 2

54

54

Now we have m = 4/5 and two points. Pick one point and proceed like in the last section.

Solve the Test Item Step 1 Find the slope of the line containing the points.

Let and.

Slope formula

Simplify.

Write an Equation Given Two Points

Step 2 You know the slope and two points. Choose one point and find the y-intercept. In this case, we chose (–3, –4).

Slope-intercept form

Replace m with –4,x with –3, and y with –4.

Multiply.

Subtract 12 from each side.

Simplify.

Write an Equation Given Two Points

Step 3 Write the slope-intercept form using

Answer: The equation is The answer is D.

Slope-intercept form

Replace m with –4 and b with –16.

Write an Equation Given Two Points