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

Point slope form: An equation of straight line with slope m and passes through one point is given by:

Given the equation:              .....[1]

On comparing with point slope form, we have;

Slope(m) =

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;

Using distributive property:

Add 4 on both sides we get;

Simplify:

Multiply both sides by we get;

x-intercept = (-1.5, 0)

Similarly for y-intercept:

Substitute the value x = 0 and solve for y;

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 as shown below in the attachment.

m∠cdf = 43° , m∠gdf = 114°, m∠gde = 23°, m∠edh = 23° , m∠cdh = 157°

step-by-step explanation:

since, it is given that de bisects the angle gdh ⇒ de divides the angle gdh into two equal angles.

⇒ m∠gde = m∠edh

⇒ 8·x   - 1 = 6·x + 5

⇒ x = 3

so, m∠gde = 8·x - 1 = 23°

and m∠edh = 23°

now, it is given ∠cde is an straight angle so, m∠cde = 180°

⇒ m∠cdf + m∠fdg + m∠gde = 180°

⇒ 43° + m∠fdg + 23° = 180°

⇒ m∠fdg = 114°

again, m∠cde = m∠cdh + m∠edh = 180°

m∠cdh + 23° = 180°

⇒ m∠cdh = 157°