Consider the equation: 5x+2y=6

Question

Consider the equation: 5x+2y=6

 

Step 1: Determine the slope & Y intercept of the equation above. 

 

Slope (m) = _______     Y Intercept = (0,__)

 

 

 

Answer 1

The Standard Form of the equation of a line looks like:   Ax + By = C

The slope-intercept form of the equation of a line looks like:  y = mx + b      [m=slope; b = y-intercept]

 

Now, if you once-and-forever change from Standard Form to slope-intercept form, you will find:

     The slope m = -A/B

     The y-intercept b= C/B

 

For the line  5x + 2y = 6

     the slope m = -5/2

     the y-intercept b= 6/2 = 3     the point (0,3)

Answer 2

solve this into the slope-intercept form

 

5x +2y = 6

 

2y = -5x +6

 

y = (-5/2)x + (6/2)

 

y = (-5/2)x + 3

 

m = -5/2   and y-intercept is (0,3)

Answer 3

Another way to do this is to find the y-intercept and x-intercept.  Then use those points to find the slope.

 

y-intercept is when x=0. 

 

5(0) + 2y = 6

 

          2y = 6

 

            y = 3

 

y-intercept = (0, 3)

 

 

x-intercept is when y=0.

 

5x + 2(0) = 6

 

5x = 6

 

  x = 6/5

 

x-intercept = (6/5, 0)

 

 

Use the two points to find the slope.

 

m = (y₂ - y₁) / (x₂ - x₁)

 

where:

Point 1 = (0, 3)

Point 2 = (6/5, 0)

 

 

m = (0 - 3) / (6/5 - 0)

m = -3 / (6/5)

m = -3 * (5/6)

m = -5/2