Question

How do i find the slope intercept form of this

Answer 1

Answer:
`\text{y} = -(2)/(3)\text{x} + (5)/(3)`

Work Shown

`\text{y} - 5 = -(2)/(3)(\text{x} + 5)\\\\\text{y} - 5 = -(2)/(3)\text{x} - (2)/(3)(5)\\\\\text{y} - 5 = -(2)/(3)\text{x} - (10)/(3)\\\\\text{y} = -(2)/(3)\text{x} - (10)/(3) + 5\\\\\text{y} = -(2)/(3)\text{x} - (10)/(3) + (15)/(3)\\\\\text{y} = -(2)/(3)\text{x} + (-10+15)/(3)\\\\\text{y} = -(2)/(3)\text{x} + (5)/(3)\\\\`

The last equation is in slope-intercept form y = mx+b

• m = -2/3 = slope
• b = 5/3 = y intercept

GeoGebra can be used to verify the answer.

Answer 2

The slope-intercept form of the given equation Y - 5 = -2/3 (X + 5) is Y = -2/3X + 5/3. The slope (m) is -2/3, and the y-intercept (b) is 5/3.

To write the given equation Y - 5 = -2/3 (X + 5) in slope-intercept form (Y = mx + b), where m is the slope and b is the y-intercept, distribute the -2/3 and simplify:

Y - 5 = -2/3X - 10/3

Add 5 to both sides:

Y = -2/3X + 5/3

So, the slope-intercept form is Y = -2/3X + 5/3. The slope (m) is -2/3, and the y-intercept (b) is 5/3.