QUESTION 1
The point-slope form equation of a line is given by:
[tex]y-y_1=m(x-x_1)[/tex]
Given slope:
[tex]m = \frac{2}{3} [/tex]
and point:(-3,5)
The point-slope form equation is:
[tex]y-5= \frac{2}{3} (x- - 3)[/tex]
This simplifies to:
[tex]y-5= \frac{2}{3} (x + 3)[/tex]
The correct option is D.
QUESTION 2
We use any two points from the table to find the required equation.
(2,14) and (4,23)
The slope is given by the formula,
[tex]m = \frac{23 - 14}{4 - 2} = \frac{9}{2} [/tex]
The equation is given by;
[tex]y-y_1=m(x-x_1)[/tex]
We plug in values to get;
[tex]y-14= \frac{9}{2} (x-2)[/tex]
Expand:
[tex]y = \frac{9}{2} x - 9 + 14[/tex]
The slope-intercept form is:
[tex]y = \frac{9}{2} x + 5[/tex]
The correct choice is B
