Linear Equation Formulas

Linear Equations Review

Slope-Intercept Form

Point-Slope Form

Standard Form

Parallel & Perpendicular Lines

Standard Form

AX + BY = C

• I can graph linear functions given a function in standard form using x and y-intercepts.

• ​I can construct linear functions in slope-intercept form.

Slope Intercept Form

Writing and Graphing Equations Using y=mx+b

Point-Slope Form

Point-Slope Equations need 2 things....

• A point

• A slope

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

Which of these represents slope-intercept form?

• y - y₁ = m(x-x₁)
• Ax + By = C
• y = mx + b

Multiple Choice

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

• $$y-1=\frac{1}{3}\left(x+4\right)$$

• $$y+4=\frac{1}{3}\left(x-1\right)$$

• $$y-4=\frac{1}{3}\left(x+1\right)$$

• $$y+1=\frac{1}{3}\left(x-4\right)$$

Multiple Choice

Find the equation that corresponds to the graph.

• y = -3/4x + 4

• y = 4/3x + 4

Multiple Choice

Determine the slope and y-intercept from the following equation:   y = 3/2x + 3

• slope: 5   y-intercept:  (0,3) 

• slope: 3/2   y-intercept:  (0,3) 

• slope:  4  y-intercept:  (0,3/2)

• slope: 1/5   y-intercept:  (0,5) 

Multiple Select

I can graph linear functions given a function in standard form using x and y-intercepts.

Select both the x and y-intercept to the following function given in standard form.

$$2x-8y=26$$  

• x-intercept =

  $$13$$  

• y-intercept =

  $$13$$  

• x-intercept =

  $$-\frac{26}{8}$$  

• y-intercept =

  $$-\frac{13}{4}$$  

Multiple Choice

If m=3 and b=6, what is the correct slope intercept equation?

• y=3-6

• y=3x-6

• y=3x+6

• y=6x+3

What if I'm given just 2 points?

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

How would you write the equation with a slope of 2/3 and a y-intercept of -3

• y=3/2x+3

• y=2/3-3

• y=2/3x-3

• y=2/3x+3

Multiple Choice

Write the equation in point-slope form for the line that contains the points

(-2, -3), (4, 3)

• y - 3 = 1(x - 2)

• y + 3 = 1(x + 2)

• y -3 = -1(x + 2)

• y + 3 = -1(x - 2)

Multiple Select

I can graph linear functions given a function in standard form using x and y-intercepts.

Select both the x and y-intercept to the following function given in standard form.

$$2x+10y=8$$  

• x-intercept =

  $$\frac{4}{5}$$  

• x-intercept =

  $$4$$  

• y-intercept =

  $$4$$  

• y-intercept =

  $$\frac{4}{5}$$  

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

Multiple Choice

What is the y-intercept in the following equation:  y=-4x-5

• -4

• -4x

• 5

• -5

Poll

Is this slope intercept form?

$$2y\ =4x\ +10$$  

• yes because it's $$y=mx+b$$  

• no, because there is a coefficient on the y.  You need to divide the entire equation by 2 first in order to get  $$y=mx+b$$  

Multiple Choice

Given m = 3 and (-2 , 5) write the equation in point-slope form.

• y + 5 = 3 (x - 2)

• y - 5 = 3 (x + 2)

Multiple Choice

What is the slope in the equation:  y=4x+3

• 3
• 4x
• 4
• x

Multiple Choice

I can graph linear functions given a function in standard form using x and y-intercepts.

The graph shown represents the function below.

$$7x-y=30$$  

• True

• False

Multiple Choice

What does "m" represent in y=mx+b?

• y-intercept

• slope

• macaroni

• nothing

Multiple Choice

What is the equation of a line when m = -7 and b = -8?

• y = -7x + 8

• y = -7x - 8

• y = 7x - 8

• y = 7x + 8

Multiple Choice

I can graph linear functions given a function in standard form using x and y-intercepts.

The graph shown represents the function below.

$$-10x+4y=30$$  

• True

• False

Multiple Choice

Which equation matches the graph?

• y= 0.5x - 5

• y= -0.5x - 5

• y= 0.5x + 5

• y= -0.5x + 5

Multiple Choice

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

• 2y = -6x + 24

• y = -3x + 12

Multiple Choice

Which equation matches the graph?

• y= 3x - 5

• y= -3x - 5

• y= 3x + 5

• y= 3x + 5

Multiple Choice

Which equation matches the graph?

• y= 3x - 5

• y= -3x - 5

• y= 3x + 5

• y= 3x + 5

Multiple Choice

Which equation matches the graph?

• y= 1x + 3

• y= 1x

• y= -1x + 3

• y= -1x

Multiple Choice

​I can construct linear functions in slope-intercept form.

Rewrite the following equation in slope-intercept form.

$$12x+10y=90$$  

• $$y=\frac{6}{5}x+10$$  

• $$y=-\frac{6}{5}x+9$$  

• $$y=-\frac{6}{5}x+4$$  

Multiple Choice

Which equation matches the graph?

• y= 1x + 3

• y= 1x

• y= -1x + 3

• y= -1x

Parallel Lines : Slopes are the same

Perpendicular Lines : Opposite Reciprocal slopes

Use point-slope and then convert to slope-intercept.

Multiple Choice

Write the equation of the line parallel to y = 3x - 4/3 through the point (-1, 2) in slope-intercept form.

• y - 2 = 3 (x +1)

• y = 3x + 5

• y = 3x + 1

Multiple Choice

Which equation matches the graph?

• y= 2x + 5

• y= 2x

• y= -2x + 5

• y= -2x

Multiple Choice

​I can construct linear functions in slope-intercept form.

Rewrite the following equation in slope-intercept form.

$$12x+9y=18$$  

• $$y=\frac{6}{5}x+10$$  

• $$y=\frac{4}{3}x+2$$  

• $$y=-\frac{4}{3}x+2$$  

Multiple Choice

Which equation matches the graph?

• y= 2x + 5

• y= 2x

• y= -2x + 5

• y= -2x