Answer:
Point slope form: An equation of straight line with slope m and passes through one point [tex](x_1, y_1)[/tex] is given by:
[tex]y-y_1=m(x-x_1)[/tex]
Given the equation: [tex]y-3 =- \frac{2}{3}(x+6)[/tex] .....[1]
On comparing with point slope form, we have;
Slope(m) = [tex]-\frac{2}{3}[/tex]
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;
[tex]0-3 =- \frac{2}{3}(x+6)[/tex]
[tex]-3 =- \frac{2}{3}(x+6)[/tex]
Using distributive property:
[tex]-3 = -\frac{2}{3}x - 4[/tex]
Add 4 on both sides we get;
[tex]-3+4 = -\frac{2}{3}x - 4+4[/tex]
Simplify:
[tex]1 = -\frac{2}{3}x[/tex]
Multiply both sides by [tex]-\frac{3}{2}[/tex] we get;
[tex]x = -\frac{3}{2} = -1.5[/tex]
x-intercept = (-1.5, 0)
Similarly for y-intercept:
Substitute the value x = 0 and solve for y;
[tex]y-3 =- \frac{2}{3}(0+6)[/tex]
[tex]y-3 =- \frac{2}{3}(6)[/tex]
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 [tex]y-3 =- \frac{2}{3}(x+6)[/tex] as shown below in the attachment.
