Forms of a line

Forms of a line

Lines have different forms depending on its applicability. The equation of the line can be expressed in

(a) Standard form

(b) Slope-intercept form

(c) point-Slope form

(d) intercepts form

Standard form of a line:

 $Ax+By=C$  

• where:

• A, B, and C are integers

• "Leading coefficient" A is positive

Standard form of a line: 

Sample Problem #1

• Graph the equation  $3x+2y=12$  

• Watch this video clip on how to graph equation of the line in standard form.

Multiple Choice

Independent Practice #1:

What is the graph of a line whose equation in standard form is

 $4x-5y=20$  

Slope-intercept form of a line:  $y=mx+b$ 

• Where: m is the slope and b is the y-intercept.

• Notes: 

• Y-intercept is a point on the graph where the line intersect (or crosses) the y-axis.  If written as an ordered pair, the x-coordinate is always equal to zero (x=0).

•  $slope=m=\frac{rise}{run}=\frac{y_2-y_1}{x_2-x_1}$  

Slope-intercept form of a line: 

Sample Problems and independent practice

• Watch this video clip on how to graph equation of the line in slope-intercept form

• Please pause the video when you are told to do. By pausing the video, You can practice doing it by yourself.

Slope-intercept form of a line: 

Independent Practice #2

• Graph the equation  $y=\frac{2}{5}x+1$ .

• Note: You can use desmos.com graphing calculator to check the graph of  $y=\frac{2}{5}x+1$ .

Multiple Choice

Independent Practice #2:

What is the graph of a line whose equation in slope-intercept form is

 $y=\frac{3}{4}x-3$  

point-slope form of a line:  $y-y_1=m\left(x-x_1\right)$ 

• Where: m is the slope and x1 and y1 are the coordinates of the given point on the line

• Notes: With given equation in point-slope form, Always flip the sign of  $x_1\ and\ y_1$  when writing an ordered pair.

•  $slope=m=\frac{rise}{run}=\frac{y_2-y_1}{x_2-x_1}$  

point-slope form of a line: 

Sample Problem

• Watch this video clip on how to graph equation of the line in point-slope form

Multiple Choice

Independent Practice #3:

What is the graph of a line whose equation in point-slope form is

 $y-5=\frac{4}{3}\left(x-1\right)$