Standard Form, Point-Slope Form, Slope-Intercept

Writing Linear Equations:

Multiple Choice

What is slope-intercept form?

• ax + by = c

• y = mx + b

• (y2-y1)/(x2-x1)

Multiple Choice

What is standard form?

• ax + by = c

• y = mx + b

• (y2-y1)/(x2-x1)

Multiple Choice

Which of these is point-slope?

• $$y-y_1=m\left(x-x_1\right)$$

• $$y=mx+b$$

• $$Ax+By=C$$

Multiple Choice

Write an equation of the line going through the point (-4, 1) with a slope of 1/3.

• $$y-1=\frac{1}{3}\left(x+4\right)$$

• $$y+4=\frac{1}{3}\left(x-1\right)$$

• $$y-4=\frac{1}{3}\left(x+1\right)$$

• $$y+1=\frac{1}{3}\left(x-4\right)$$

We also learned how to transform Point-Slope equations into Slope Intercept form.

Multiple Choice

Transform this point-slope equation into slope intercept form:

$$y-2=3\left(x+4\right)$$  

• y=1/3x+14

• y = 3x + 12

• y = 3x+14

• y= 1/3x+14

Point-slope Form: y - y₁ = m( x - x₁)

• Useful when you are given a point (x₁, y₁) and slope (m)

• Plug in the opposite values of points into formula

Multiple Choice

What is the equation in Point-Slope form that goes through the point (6,1) and has a slope of -3?

• y - 6 = -3(x - 1)
• y + 6 = -3(x + 1)
• y - 1 = -3(x - 6)
• y + 1 = -3(x + 3)

Multiple Choice

What is the equation in Point-Slope form that goes through the point (-2,4) and has a slope of 3?

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

Multiple Choice

Write the equation of the line using point-slope if the slope is -3 and it goes through the point (10,5).

• y - 5 = -3 ( x - 10)

• y = -3x + 35

• y + 5 = -3 ( x + 10)

• y = -3x - 35

Standard Form is one of three key ways we write linear functions.

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In the visual to the right, we have the general equation of Standard Form. A, B, and C represent integers, while x and y are variables.

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Standard Form

Multiple Choice

Convert the following standard form equation to slope-intercept (y=mx+b).

• 2y = -6x + 24

• y = -3x + 12

• y=-6x+24

• y=-3x+24

Multiple Choice

Find the Slope

(-4 , 6) and (2 , -2)

• $$\frac{1}{2}$$  

• 6 

•  -4/3

• 2

Multiple Choice

(-5, -2) and (0, -1)

• y=1/5x-2
• y=1/5x+1
• y=1/5x+3
• y=1/5x-1

Multiple Choice

 (1, 2) and (-2, 5)

• y=x+3
• y=-x+3
• y=-x+1
• y=3x+3