Question

Write an equation in slope-intercept form from the points (0, 3) and (-4,-1)

Answer 1

y = x + 3

Explanation:

Slope-intercept form is represented by the formula
`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 line. Use the slope formula
`m = (y_2-y_1)/(x_2-x_1)` and substitute the x and y values of the given points into it. Then, simplify to find the slope, or
`m`:

`m = ((-1)-(3))/((-4)-(0)) \\m = (-1-3)/(-4-0) \\m = (-4)/(-4) \\m = 1`

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
`y-y_1=m(x-x_1)` and substitute values for
`m`,
`x_1`, and
`y_1`. From there, we can convert the equation into slope-intercept form.

Since
`m` represents the slope, substitute 1 in its place. Since
`x_1` and
`y_1` 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:

`y-3=1(x-0)\\y-3 = x\\y = x + 3`