Applied Linear Equations 1


Useful formulas to know:
Slope formula
m = y2 - y1
x2 - x1
  where (x1, y1) and (x2, y2) are two points on the line

Slope-intercept form

y = mx + b   where m is the slope

Point-slope form

y - y1 = m (x - x1 )   where m is the slope and (x1 , y1) is a point on the line


Example 1: Slope and point

Solve. Answer using slope-interecept form.
In slope-intercept form, write the equation of a line that goes through point (-2, 1) with slope 5.
Equation:

y = mx + b 1. Take what you know and plug it into the slope-intercept formula.
1 = 5(-2) + b   m = 5 and (x, y) = (-2, 1)
1 = -10 + b 2. Solve for b
11 = b  
 
y = 5x + 11 3. Plug m and b into the slope-intercept formula for the answer
The answer is


Example 2: Two points

Solve. Answer using slope-interecept form.
In slope-intercept form, write the equation of a line that goes through point (0, -2) and (2, -5).
Equation:

1. Calculate the slope using (x1, y1) = (0, -2) and (x2, y2) = (2, -5)
m = y2 - y1
x2 - x1
= -5 - (-2)
2 - 0
= -3
2
2. Take what you know and plug it into the point-slope formula
y - y1 = m (x - x1 )
y - (-2) = -3
2
(x - 0)
3. Put the equation in slope-intercept form by solving for y
y + 2 = -3
2
x
y = -3
2
x - 2
The answer is

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