Answer:
point-slope form: [tex]y-3=-\frac{1}{3}(x - 3)[/tex]
slope-intercept form: [tex]y=-\frac{1}{3}x+4[/tex]
Step-by-step explanation:
point-slope form is: y - y1 = m(x - x1)
slope-intercept form is: y = mx + b
The formula used to find the slope(m): [tex]\frac{y2-y1}{x2-x1}[/tex]
(x1, y1) = (3, 3)
(x2, y2) = (-6, 6)
The first thing we need to do to write the equations is to find the slope. We can do this by inputting the given points into the slope formula:
[tex]\frac{6-3}{-6-3}[/tex]
Simplify:
6 - 3 = 3
-6 - 3 = -9
[tex]\frac{3}{-9} =-\frac{1}{3}[/tex]
The slope is [tex]-\frac{1}{3}[/tex]. We can now write the equation in point-slope form:
[tex]y-3=-\frac{1}{3}(x - 3)[/tex]
To write the equation in slope-intercept form, we need to find the value of b. To find its value, input the value of the slope and one point into the equation for slope-intercept form:
y = mx + b
3 = [tex]-\frac{1}{3}[/tex](3) + b
Now you can solve for b:
3 = [tex]-\frac{1}{3}[/tex](3) + b
3 = -1 + b
4 = b
Now that we know the value of b, we can write the equation in slope-intercept form:
[tex]y=-\frac{1}{3}x+4[/tex]
I hope this helps. :)
