Answer:
Step-by-step explanation:
Point-slope form:
The standard point-slope form equation is
[tex]y-y_1=m(x-x_1)[/tex]
where [tex](x_1,y_1)[/tex] are the coordinates and [tex]m[/tex] is the slope/gradient
so for point-slope form we need to find m cause we already have 2 coordinates (-3,5) , (3,3) we can use any one of them in our equation but first we need to find the slope by the formula
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
we use our coordinates to find it and simply plug in the values
[tex]m=\frac{3-5}{3-(-3)} \\m=\frac{-2}{6} \\\\m=\frac{-1}{3}[/tex]
so we get our slope m = -1/3
and simply put m and any one of the coordinates into the standard form
[tex]y-y_1=m(x-x_1)\\y-3=\frac{-1}{3} (x-3)\\3(y-3)=-1(x-3)\\3y-9=-x+3\\3y=-x+12\\y=\frac{-x+12}{3} \\y=\frac{-x}{3} +4[/tex]
Slope-intercept form:
The standard slope-intercept form is
[tex]y=mx+c[/tex]
where m is the slope and c is the y-intercept, we already know the slope is -1/3 from the previous steps but we don't know the y-intercept so lets get started.
y-intercept means the equation intersects the y-axis which means the coordinate should be [tex](0,y)[/tex] so we plug in the slope -1/3 and the coordinate given above (-3,5) , (3,3) in the equation to find the y-intercept that is c. We can you use any one of the two coordinates.
[tex]y=mx+c\\3=\frac{-1}{3}(3)+c \\\\3=\frac{-3}{3} +c\\\\3=-1+c\\c=4[/tex]
so now we found the value of c=4 which is the y-intercept (0,4) and finally our slope-intercept form would be
[tex]y=\frac{-x}{3} +4[/tex]
as both form are same but the approach is different this verifies that both our answers are correct.
