A.6 Point-Slope and Standard Form

Linear Equations Review

Slope-Intercept Form

Point-Slope Form

Standard Form

Parallel & Perpendicular Lines

Slope-Intercept: y = mx+b

• Used for graphing linear equations

• Need a slope (m) and y-intercept (b)

Multiple Choice

Find the equation that corresponds to the graph.

• y = -3/4x + 4

• y = 4/3x + 4

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

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

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

• $$y-1=\frac{1}{3}\left(x+4\right)$$

• $$y+4=\frac{1}{3}\left(x-1\right)$$

• $$y-4=\frac{1}{3}\left(x+1\right)$$

• $$y+1=\frac{1}{3}\left(x-4\right)$$

Fill in the Blanks

Name the slope of this line:

$y+1=-\frac{5}{4}\left(x-3\right)$  

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

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  $$y=mx+b$$  

Fill in the Blanks

Transform this point-slope equation into slope intercept form:

$y-2=3\left(x+4\right)$  

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)

Standard Form : Ax + By = C

• Form is useful to convert to a different form.

• A, B, and C are all whole numbers.

Multiple Choice

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

• 2y = -6x + 24

• y = -3x + 12