Question

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

Answer 1

Answer:

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:  $y-3 =- \frac{2}{3}(x+6)$            .....[1]

On comparing with point slope form, we have;

Slope(m) = $-\frac{2}{3}$

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;

$0-3 =- \frac{2}{3}(x+6)$

$-3 =- \frac{2}{3}(x+6)$

Using distributive property:

$-3 = -\frac{2}{3}x - 4$

Add 4 on both sides we get;

$-3+4 = -\frac{2}{3}x - 4+4$

Simplify:

$1 = -\frac{2}{3}x$

Multiply both sides by $-\frac{3}{2}$ we get;

$x = -\frac{3}{2} = -1.5$

x-intercept = (-1.5, 0)

Similarly for y-intercept:

Substitute the value x = 0 and solve for y;

$y-3 =- \frac{2}{3}(0+6)$

$y-3 =- \frac{2}{3}(6)$

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 $y-3 =- \frac{2}{3}(x+6)$ as shown below in the attachment.

Answer 2

The slope is - 2/3

The Y-Intercept is - 1