Answer:
y = -3x + 3
Step-by-step explanation:
Slope-intercept form is represented by the equation y = mx + b. We can write an equation in point-slope form first, then convert it to that form.
1) First, find the slope of the equation. Use the slope formula [tex]m = \frac{y_2-y_1}{x_2-x_1}[/tex] and substitute the x and y values of the given points into it. Then, simplify:
[tex]m = \frac{(-6)-(3)}{(3)-(0)}\\m = \frac{-6-3}{3-0}\\m = \frac{-9}{3}\\m = -3[/tex]
Thus, the slope is -3.
2) Now, use the point-slope formula, [tex]y-y_1 = m (x-x_1)[/tex] and substitute values for [tex]m[/tex], [tex]x_1[/tex], and [tex]y_1[/tex]. From there, we can isolate y to convert the equation into slope-intercept form.
Since [tex]m[/tex] represents the slope, substitute -3 in its place. Since [tex]x_1[/tex] and [tex]y_1[/tex] represent the x and y values of one point the line intersects, choose any one of the given points (either one is fine) and substitute its x and y values into the formula, too. (I chose (0,3), as shown below). Finally, isolate y to find the answer:
[tex]y-3 = -3(x-0)\\y-3 = -3x\\y = -3x + 3[/tex]
