Question

Find the slope (m) and the y-intercept (b) of each line. Make sure the equation is I slope/intercept form first.1) y= 3/2x+42) y= 1/2x-13) y= -2/5x-34) y= -5/4x+15) y= -26) x+y= 37) 4x-y= -48) x+5y= -159) 4x-5y= 1010) 5x+2y= -8

Answer 1

Notice that for the first FIVE equations, the actual lines are in the "slope-intercept form" so it os very easy to give the slope and the intercept for then:

1) m = 3/2 ; b = 4 equation: y = 3/2 x + 4

2) m = 1/2 ; b = -1 equation: y = 1/2 x - 1

3) m = -2/5 ; b = -3 equation: y = -2/5 x - 3

4) m= -5/4 ; b = 1 equation: y = -5/4 x + 1

5) m= 0 ; b = -2 equation: y= 0 x - 2

For the rest, we need to solve for y to make the "m" (slope, and the "b" (intercept) more evident. So we work as follows:

6) x+ y = 3

subtract "x" from both sides

y = - x + 3 therefore m = -1 ; b = 3

7) 4 x - y = - 4

add "y" to both sides

4 x = y - 4

add 4 to both sides

4 x + 4 = y

therefore m = 4 ; b = 4

8) x + 5 y = - 15

subtract x from both sides

5 y = - x - 15

divide everything on both sides by 5 to isolate "y"

y = - 1/5 x - 15/5 = - 1/5 x - 3

therefore m = -1/5 ; b= -3

9) 4 x - 5 y = 10

add 5 y to both sides

4 x = 5 y + 10

subtract 10 from both sides

4 x - 10 = 5 y

divide both sides by 5 to isolate y

4/5 x - 10/5 = y

y = 4/5 x - 2

therefore m= 4/5 ; b = -2

10) 5 x + 2 y = - 8

subtract 5 x from both sides

2 y = - 5 x - 8

divide both sides by 2

y = - 5/2 x - 8/2

y = - 5/2 x - 4

therefore m = - 5/2 ; b = -4

All the equations are in bold