Question

How can I find the line passing through the points (7,16) and (2,-4)

Answer 1

We can solve for the line in point-slope form:

• $y-y_1=m(x-x_1)$

where $(x_1,y_1)$ is some point the line passes through and m is the slope.

First, to find the equation of any line, we need to find the slope. We can use the following formula to solve for the slope.

• $m = \dfrac{y_2-y_1}{x_2-x_1}$

where $(x_2,y_2)$ and $(x_1, y_1)$ are two different points that the line passes through.

Let's use the points we are given, (7,16) and (2,-4)

• $m = \dfrac{16-(-4)}{7-2}$

• $=\dfrac{20}{5}=4$

The line has a slope of 4, m=4.

Now we can put the value of m=4 into the following equation:

• $y-y_1=m(x-x_1)$

However, we still need a value for $x_1$ and $y_1$. To determine their values, you can choose any of the two points. I'll be using (7,16).

Thus, $x_1=7$ and $y_1=16$. Inserting these values, along with the value for m, into the point-slope form equation gives us:

• $y-16=4(x-7)$

This should be the equation of the line passing through points (7,16) and (2,-4).

If you need the line in any of the other forms, such as

1. Slope intercept form: $y=mx+b$
2. or Standard form: $Ax+Bx=C$,

just use the point-slope form equation I gave and change it so it resembles the form you need. If you need any help with that, I'd be happy to assist you.

Welcome to Brainly and happy studying!

~ Padoru