Respuesta :

Padoru

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

  • [tex]y-y_1=m(x-x_1)[/tex]

where [tex](x_1,y_1)[/tex] 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.

  • [tex]m = \dfrac{y_2-y_1}{x_2-x_1}[/tex]

where [tex](x_2,y_2)[/tex] and [tex](x_1, y_1)[/tex] are two different points that the line passes through.

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

  • [tex]m = \dfrac{16-(-4)}{7-2}[/tex]
  • [tex]=\dfrac{20}{5}=4[/tex]

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

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

  • [tex]y-y_1=m(x-x_1)[/tex]

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

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

  • [tex]y-16=4(x-7)[/tex]

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: [tex]y=mx+b[/tex]
  2. or Standard form: [tex]Ax+Bx=C[/tex],

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

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