Question

Find the slope and they intercept of the line : 2x-3y+5 ​

Answer 1

Answer:

2x+3y+5=0 is in General Slope form now put it into Slope form y=mx +b

3y +2x + ( ➖2x) +5 + ( ➖ 5) = 0 ➖2x ➖5 subtracting 2x and 5 from the left side of the equation let's do that to the right side as well

3y = - 2x - 5 we have to isolate y. Now ➗ left side of the equation and ➗ the right side as well by 3

3y/3 = - 2x/3 - 5/3 rewrite into Slope Form y=mx +b m = slope = rise/run= Δy/ Δx = (y2 - y1) /(x2-x1)

y = - 2/3x - 5/3

∴ recognizing slope = m = - 2/3 and b = - 5/3 = 1.6666666

Now solve for the y-intercept, so let is x = 0

y = - 2/3(0) - 5/3

y = - 5/3

∴ y = - 5/3 = b = y-intercept. When x equals zero then y equals - 5/3 or (0,-5/3). Now find that point and mark it on your graph

Now solve for x-intercept, so let y = 0

y = - 2/3x - 5/3

0 = - 2/3x - 5/3 multiply everything by 3 to cancel out the denominators

(3)0 = - (3)2/3x - (3)5/3

0 = - 2x - 5

-2x - 5 = 0

-2x = 5 now ➗ both sides by - 2 now to isolate x

2x/-2 = 5/-2 solve

x = - 5/2 ∴ x - intercept is = - 5/2 = - 2.5

slope = m = - 2/3

x - intercept = - 5/2 = - 2.5 when y = 0

y-intercept or b = - 5/3 = - 1.666 when x = 0

Answer 2

Answer:

$\\ x \: \: inter cept \: \: = - \frac{5}{2} \\ \\ \\ y \: \: \: intercept \: \: = \: \: \frac{5}{3} \\ \\ slope \: \: \: \: \: \: \: \: \: \: \: \: = \frac{2}{3}$

Step-by-step explanation:

$2x - 3y + 5 = 0 \\ 3y = 2x + 5 \\ y = \frac{2}{3 } x + \frac{5}{3} \\ \\ \\ slope = \frac{2}{3} \\ \\ 2x - 3y = - 5 \\ \\ \frac{x}{ \frac{ - 5}{2} } + \frac{y}{ \frac{5}{3} } = 1 \\ \\ \\ x \: \: inter cept \: \: = - \frac{5}{2} \\ \\ \\ y \: \: \: intercept \: \: = \: \: \frac{5}{3}$