Answer:
y = x + 3
Step-by-step explanation:
Slope-intercept form is represented by the formula [tex]y = mx + b[/tex]. We can write an equation in point-slope form first, then convert it to that form.
1) First, find the slope of the line. 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 to find the slope, or [tex]m[/tex]:
[tex]m = \frac{(-1)-(3)}{(-4)-(0)} \\m = \frac{-1-3}{-4-0} \\m = \frac{-4}{-4} \\m = 1[/tex]
Thus, the slope of the line must be 1.
2) Now, since we know a point the line intersects and its slope, 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 convert the equation into slope-intercept form.
Since [tex]m[/tex] represents the slope, substitute 1 in its place. Since [tex]x_1[/tex] and [tex]y_1[/tex] represent the x and y values of a point the line intersects, choose any one of the given points (either one is fine) and substitute its x and y values into the equation, too. (I chose (0,3).) Finally, isolate y to find the answer:
[tex]y-3=1(x-0)\\y-3 = x\\y = x + 3[/tex]
