3.6 Equations of Lines

What is the slope of the given points?

(9,−4),(4,−6)

Write the slope-intercept form of the equation of each line given the slope and y-intercept.

 $Slope=-\frac{2}{3}$   $y-intercept=5$  

• $y=\frac{2}{3}x+5$

• $y=-\frac{5}{3}x+5$
  

• $y=-\frac{2}{3}x+5$
  

• $y=-x+5$
  

What is the slope of the given points?

(-15, -6), (-18, -19)

Write the slope-intercept form of the equation of each line given the slope and y-intercept.

 $Slope\ =4$   $y-intercept\ =3$  

• $y=4x-3$

• $y=3x+4$
  

• $y=-3x+4$
  

• $y=-4x-3$
  

Write the point-slope form of the equation of the line through the given point with the given slope. $through:(-5,3)$   

 $slope=-\frac{3}{5}$ 

 

•  $y-3=-\frac{3}{5}\left(x+5\right)$  
  

•  $y-3=4\left(x-5\right)$  

•  $y-5=\frac{3}{5}\left(x-3\right)$  

•  $y-3=-4\left(x+5\right)$  

Write the point-slope form of the equation of the line through the given point with the given slope.

 $through\ \left(1,5\right)\ \ \ \ slope\ =\ 9$ 

•  $y-1=-9\left(x-5\right)$  
  

•  $y-5=9\left(x-1\right)$  

•  $y+1=-9\left(x+5\right)$  

•  $y+5=-9\left(x+1\right)$  

Write the point-slope form of the equation of the line through the given point with the given slope.

 $through:\ \left(5,-1\right)\ \ \ \ \ slope\ =\frac{2}{5}$   

•  $y+1=-\frac{1}{5}\left(x-5\right)$  
  

•  $y-1=\frac{2}{5}\left(x+5\right)$  

•  $y+1=\frac{2}{5}\left(x-5\right)$  

•  $y+1=x-5$  

Write the slope-intercept form of the equation of the line through the given points.

(-3,4) and (5,1)

HINT:  Calculate Slope.  Write in Point-Slope Form.  Convert.

• $y=-\frac{23}{8}x+\frac{3}{8}$

•  $y=-\frac{3}{8}x+\frac{23}{5}$ 

• $y=-\frac{1}{2}x-\frac{3}{8}$

•  $y=-\frac{3}{8}x+\frac{23}{8}$  

Write the point-slope form of the equation of the line through the given point with the given slope.

 $through:\ \left(-5,4\right)\ \ \ \ \ slope\ =\frac{1}{5}$   

•  $y+4=\frac{1}{5}\left(x+5\right)$  
  

•  $y-5=-\frac{1}{15}\left(x+4\right)$  

•  $y-4=-\frac{1}{5}\left(x+5\right)$  

•  $y-4=\frac{1}{5}\left(x+5\right)$  

Write the slope-intercept form of the equation of the line through the given point with the given slope.

 $through:(-1,1),\ \ \ slope=-5$  
HINT: Write in point slope 1st

•  $y=-5x-4$  

•  $y=-4x+5$  

•  $y=4x+5$  

•  $y=5x-4$