Question

Write the equation in point-slope form of the line that passes through the given points. Then write the equation in slope-intercept form.
(-6,6),(3,3)

Answer 1

Answer:

point-slope form:  $y-3=-\frac{1}{3}(x - 3)$

slope-intercept form: $y=-\frac{1}{3}x+4$

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): $\frac{y2-y1}{x2-x1}$

(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:

$\frac{6-3}{-6-3}$

Simplify:

6 - 3 = 3

-6 - 3 = -9

$\frac{3}{-9} =-\frac{1}{3}$

The slope is $-\frac{1}{3}$. We can now write the equation in point-slope form:

$y-3=-\frac{1}{3}(x - 3)$

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 = $-\frac{1}{3}$(3) + b

Now you can solve for b:

3 = $-\frac{1}{3}$(3) + b

3 = -1 + b

4 = b

Now that we know the value of b, we can write the equation in slope-intercept form:

$y=-\frac{1}{3}x+4$

I hope this helps. :)