Answer:
Point-slope form:
[tex]\displaystyle y-3=-\frac{1}{3}(x-3)[/tex]
Slope-intercept form:
[tex]\displaystyle y=-\frac{1}{3}x+4[/tex]
Step-by-step explanation:
We want the equation in point-slope form and slope-intercept form that passes through the points (-3, 5) and (3, 3).
First, we will find the slope between the two points. By the slope formula:
[tex]\displaystyle m=\frac{5-3}{-3-3}=\frac{2}{-6}=-\frac{1}{3}[/tex]
Point-slope form is given by:
[tex]\displaystyle y-y_1=m(x-x_1)[/tex]
We can choose either point. I'm going to let (3, 3) be (x₁, y₁). The slope m is -1/3. Therefore:
[tex]\displaystyle y-3=-\frac{1}{3}(x-3)[/tex]
Is the point-slope form*.
To find the slope-intercept form, we simply need to isolate y. Distribute:
[tex]\displaystyle y-3=-\frac{1}{3}x+1[/tex]
Adding 3 to both sides yields:
[tex]\displaystyle y=-\frac{1}{3}x+4[/tex]
This is slope-intercept form.
*If you use the other point, the point-slope form will be:
[tex]\displaystyle y-5=-\frac{1}{3}(x+3)[/tex]
