Question

Which is the graph of y-3 = -2/3(x +6)?

Answer 1

The slope is - 2/3

The Y-Intercept is - 1

Answer 2

Point slope form: An equation of straight line with slope m and passes through one point
`(x_1, y_1)` is given by:

`y-y_1=m(x-x_1)`

Given the equation:
`y-3 =- (2)/(3)(x+6)` .....[1]

On comparing with point slope form, we have;

Slope(m) =
`-(2)/(3)`

Since, slope of line is negative means i.,e it is trending downward from left to right.

Now, find the intercept of this equation:

x-intercept: The graph or line crosses the x-axis i.e,

Substitute y = 0 in [1] and solve for x;

`0-3 =- (2)/(3)(x+6)`

`-3 =- (2)/(3)(x+6)`

Using distributive property:

`-3 = -(2)/(3)x - 4`

Add 4 on both sides we get;

`-3+4 = -(2)/(3)x - 4+4`

Simplify:

`1 = -(2)/(3)x`

Multiply both sides by
`-(3)/(2)` we get;

`x = -(3)/(2) = -1.5`

x-intercept = (-1.5, 0)

Similarly for y-intercept:

Substitute the value x = 0 and solve for y;

`y-3 =- (2)/(3)(0+6)`

`y-3 =- (2)/(3)(6)`

Simplify:

y -3 = -4

Add 3 on both sides, we get;

y-3+3 = -4+3

Simplify:

y = -1

y-intercepts = (0, -1)

Now, using these points we get a graph of the equation
`y-3 =- (2)/(3)(x+6)` as shown below in the attachment.