Slop of a line

Question

Consider the line with equation 3y+5x=-6
Rewrite the equation in slope-intercept form.

State the slope of the line.

Write the x-intercept and y-intercept as ordered pairs.

Using algebra, determine whether (-3, 3) lies on this line.

Answer 1

3y + 5x = 6

 

to rewrite this equation in the form y = mx + b, solve the equation for y.  Whatever the coefficient of x is is the slope.

 

3y + 5x - 5x = -5x - 6 (subtract 5x from both sides)

 

3y/3 = (-5x - 6)/3 (divide both sides by 3 to isolate the variable y)

 

y = -5x/3 - 2

 

slope = -5/3

 

To determine if the point (-3,3) lies on the line, substitute -3 for x and 3 for y.  

3(3) + 5(-3) = -6

Answer 2

3y + 5x = -6

3y = -5x - 6

y = (-5/3)x - 2

m = -5/3,  b = -2

y-intercept: (0,-2)

Let y = 0, 3(0) + 5x = -6

x = -6/5

x-intercept: (-6/5,0)

(-3,3)

3(3) + 5(-3) = -6

9 - 15 = -6

-6 = -6

So, the point lies on the line.