Writing the Equation of a Line given Two Points

Writing the Equation of a Line Given Two Points

Multiple Choice

Which equation is in slope-intercept form?

• $2x+3y=8$

• $y-5=3\left(x-4\right)$

• $y=3x+4$

Multiple Choice

Which equation has a slope of 1/3 and a y-intercept of 2

•  $y=\frac{1}{3}x+2$ 

•  $y=2x+\frac{1}{3}$ 

•  $\frac{1}{3}=m2+b$ 

Multiple Choice

Which equation has a slope of -1 and a y-intercept of 8

•  $y=8x-1$ 

•  $y=-1m-8$ 

•  $y=-x+8$ 

Multiple Choice

Substitute in a slope of -1/2 and (-1,3) into  y=mx+b

•  $-1=-\frac{1}{2}\left(3\right)+b$ 

•  $3=-\frac{1}{2}\left(-1\right)+b$ 

•  $-\frac{1}{2}=-1\left(3\right)+b$ 

Open Ended

Substitute in a slope of -5 and the point (4,-1) into y=mx+b

Multiple Choice

Solve for b:

-1=-5(4) + b

• b = -21

• b =19

• b = 1/20

Open Ended

Slope: -5

Y- Intercept (b): 19

Write the equation of this line in slope-intercept form.

Open Ended

Substitute in a slope of -4/5 and the point (5,-1) into y=mx+b

Multiple Choice

Solve for b:

 $-1=-\frac{4}{5}\left(5\right)+b$  

• b = -2

• b = 3

• b = -5

Open Ended

Slope:  $-\frac{4}{5}$  

y-intercept: 3

Write an equation in slope-intercept form.
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Let's Practice

• Go to Schoology

• Go to This Week's Work

• Open the Point and Slope Practice

Today's Goals

• Write the equation of a line in Slope-Intercept Form (y = mx + b) given two points.

Poll

What do you need to write the equation of a line in slope-intercept form (y = mx + b)

• Just the slope!

• Just one point!

• a slope and a y-intercept

So... How do we do this?

Let's do one together

One Step at a Time... >

Find the equation fo the line that goes through points:

(-4, -4) and (4,6)

Multiple Choice

Step 1: Calculate the Slope(m) from the points:

(-4,-4) and (4, 6)

• $m=\frac{\left(6\right)-\left(-4\right)}{\left(4\right)-\left(-4\right)}=\ \frac{10}{8}=\frac{5}{4}$

• $m=\frac{\left(6\right)-\left(4\right)}{\left(4\right)-\left(4\right)}=\ \frac{2}{0}=\ undefined$

• $m=\frac{\left(4\right)-\left(-4\right)}{\left(6\right)-\left(-4\right)}=\ \frac{8}{10}=\frac{4}{5}$

Multiple Choice

Step 2: Plug in the slope (5/4) and the x and y of one of the points (4,6) into y=mx+b:

•  $4\ =\ \frac{5}{4}\left(6\right)+b$ 

•  $6=\frac{5}{4}\left(4\right)+b$ 

•  $b=\frac{5}{4}\left(4\right)+6$ 

Multiple Choice

Step 3: Simplify 

 $6=\frac{5}{4}\left(4\right)+b$  

•  $6\ =\ \frac{5}{4}+b$ 

•  $6=5\ +\ b$ 

•  $6=4+b$ 

Multiple Choice

Step 4: Solve for b

 $6=5+b$  

•  $b=11$ 

•  $b=1$ 

•  $b=\frac{6}{5}$ 

Multiple Choice

Step 5: Use the slope of 5/4 and the y-intercept 1 to write the equation of the line in slope-intercept form:

 $y=mx+b$ 

•  $y=\frac{5}{4}x+1$ 

•  $y=1x+\frac{5}{4}$ 

Let's Look at the Steps Again...

• 1. Use the two points to find the slope

• 2. Plug the slope and the x and y of one point into y=mx + b

• 3. Solve for b

• Rewrite y = mx + b using the slope(m) and the y-intercept(b)

Multiple Choice

Write the equation of a line that passes through points ( 4, 7) and

( 8, 10)

• $y=3x+4$

• $y=8x+10$

• $y=\frac{3}{4}x\ +4$

• $y=-\frac{3}{4}x+4$

Multiple Choice

Write the equation of a line that passes through points ( - 1, 0) and

(1, - 10).

• $y=-5x-5$

• $y=-\frac{1}{5}x\ -5$

• $y=-5$

• $y=5x+5$

Independent Work

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• Go to Today's Work in Schoology

• Click on the Independent Practice Assignment.

• You have 20 minutes to complete and submit