Question

When the equation `y=5x+p` is a constant, is graphed in the `xy`-plane, the line passes through the point (-2,1). what is the value of p?

Answer 1

`p=11`

Explanation:

Our line is in the form of `y=mx+b`, where `m` is the slope and `b` is the `y`-coordinate of the `y`-intercept, `(0,b)` .

Here, we can see `m=5` and `b=p`.

Recall the formula for the slope:

`m=(y_2-y_1)/(x_2-x_1)`

Where `(x_1,y_1)` and `(x_2,y_2)` are two points through which the line with this slope passes.

`m=5`:

`5=(y_2-y_1)/(x_2-x_1)`

We are given a point through which the line passes, `(-2,1)`, so `(x_1,y_1)=(-2,1)`

Since `b=p`, we know our `y`-intercept for this line is `(0,p)`. The y-intercept is certainly a point through which the line passes. So, `(x_2,y_2)=(0,p)`

Let's rewrite our slope equation with all of this information:

`5=(p-1)/(0-(-2))`

We now have an equation with one unknown variable, `p,` for which we can solve:

`5=(p-1)/2`

`5(2)=(p-1)`

`10=p-1`

`p=11`

Answer 2

`p = 11`

Explanation:

Here's a different way. We know that the point `(-2, 1)` lies on the graph. Therefore

`1 = 5(-2) + p`

`1 = -10 + p`

`11 =p`

As derived by the other contributor.

Hopefully this helps!