Writing the Equation of a Line from Two Points

SLOPE and Y-intercept

• An equation is written as y=mx + b

• m= Slope

• b= y intercept

Poll

Which questions can you answer correctly by now?

Reorder

When finding the equation of line between two points, what order must you follow?

• Find the slope (average rate of change) between the 2 points

• Substitute the $$m$$ , or slope, into the equation $$y=mx+b$$

• Substitute an $$x\ and\ y$$ coordinate into the equation $$y=mx+b$$

• Solve for $$b$$

• Substitute the $$m$$ and $$b$$ into $$y=mx+b$$ form of a line

1

2

3

4

5

• 1
• 2
• 3
• 4
• 5

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Fill in the Blank

When writing the slope-intercept form of the equation of the line through the given points $$\left(3,2\right)\ and\ \left(2,4\right)$$ you discover that the rate of change, or slope, is_

Fill in the Blank

When writing the slope-intercept form of the equation of the line through the given points $$\left(3,2\right)\ and\ \left(2,4\right)$$ you discover that the slope, is $$-2.$$ You then substitute the slope and first point into the equation $$2=-2\left(3\right)+b$$ and find that $$b=$$

Drag and Drop

When writing the slope-intercept form of the equation of the line through the given points $$\left(3,2\right)\ and\ \left(2,4\right)$$ you discover that the slope is $$m=-2.$$ You then substitute the slope and first point into the equation $$2=-2\left(3\right)+b$$ and find that $$b=8$$ .

The equation of the line is ​

Placeholder

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Fill in the Blank

When writing the slope-intercept form of the equation of the line through the given points $$\left(-1,3\right)\ and\ \left(1,-1\right)$$ you discover that the rate of change, or slope, is_

Fill in the Blank

When writing the slope-intercept form of the equation of the line through the given points $$\left(-1,3\right)\ and\ \left(1,-1\right)$$ you discover that the slope, is $$-2.$$ You then substitute the slope and first point into the equation $$3=-2\left(-1\right)+b$$ and find that $$b=$$

Drag and Drop

When writing the slope-intercept form of the equation of the line through the given points $$\left(-1,3\right)\ and\ \left(1,-1\right)$$ you discover that the slope, is $$-2.$$ You then substitute the slope and first point into the equation $$3=-2\left(-1\right)+b$$ and find that $$b=1.$$

Which is the correct equation of the line?​

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Multiple Choice

Which equation represents the line that passes through the points $$\left(-3,7\right)$$ and $$\left(3,3\right)$$ ?

• $$y=\frac{2}{3}x+1$$

• $$y=\frac{2}{3}x+9$$

• $$y=-\frac{2}{3}x+5$$

• $$y=-\frac{2}{3}x+9$$

Multiple Choice

What is an equation for the line that passes through the coordinates $$\left(2,0\right)$$ and $$\left(0,3\right)$$ ?

• $$y=-\frac{3}{2}x+3$$

• $$y=-\frac{3}{2}x-3$$

• $$y=-\frac{2}{3}x+2$$

• $$y=-\frac{2}{3}x-2$$

Multiple Choice

Which equation represents the line that passes through the points $$\left(1,1\right)$$ and $$\left(-2,7\right)$$ ?

• $$y=-2x+9$$

• $$y=-2x+3$$

• $$y=-\frac{1}{2}x+8$$

• $$y=-\frac{1}{2}x+6$$

Multiple Choice

What is an equation of the line that passes through the points $$\left(2,1\right)$$ and $$\left(6,-5\right)$$ ?

• $$y=-\frac{3}{2}x-2$$

• $$y=-\frac{3}{2}x+4$$

• $$y=-\frac{2}{3}x-1$$

• $$y=-\frac{2}{3}x+\frac{7}{3}$$

Multiple Choice

What is an equation of the line that passes through $$\left(-2,3\right)$$ and $$\left(6,1\right)$$ ?

• $$y=-\frac{1}{2}x+2$$

• $$y=-\frac{1}{2}x+4$$

• $$y=2x+7$$

• $$y=2x-1$$

Multiple Choice

What is the y- intercept of the graph of y = -5x + 6

• 5

• -5

• 6

• -6

Multiple Choice

What is the y-intercept of the line graphed below?

• 3

• 4

• -3

• 4/3

Multiple Choice

Which equation represents the following graph?

• y = 3x + 2

• y = -2x + 3

• y = 2x + 3

• y = -3x + 2

Multiple Choice

Which equation is being represented by this line?

• y = -1x + 2

• y = 1/2x + 2

• y = 3x -4

• y = -3x +2

Multiple Choice

What does the "b" stand for in y=mx+b?

• slope

• x-intercept

• y-intercept

Multiple Choice

What letter represents the slope of a line in the equation y = mx + b?

• y

• m

• x

• b

Multiple Choice

What is the y-intercept, also known as the "b" value, of the line y = 4x + 10?

• 4

• 14

• 10

• Spring Break

Multiple Choice

Find the slope

• -5/7

• 7/5

• -7/5

• 5/7

Multiple Choice

Write the equation of the line.

• y = x + 1
• y= x - 1
• y= -x + 1
• y= -x - 1