Question

PLEASE HELP ME WITH THIS QUESTION ASAP

Answer 1

Answer: 4x + y = 13

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Step-by-step explanation:

Let's use point slope form to get

y - y1 = m(x - x1)

y - y1 = -4(x - x1) .... plug in the given slope m = -4

y - 5 = -4(x - 2) .... plug in the given point (x1,y1) = (2,5)

Now we isolate y

y - 5 = -4(x - 2)

y - 5 = -4x + 8

y = -4x + 8 + 5

y = -4x + 13

This equation is in slope intercept form y = mx+b

m = -4 is the slope

b = 13 is the y intercept

To get this into standard form, we add 4x to both sides so that the x and y terms are on the left side

y = -4x+13

y+4x = 13

4x + y = 13 is the final answer

This is in standard form Ax+By = C where

A = 4

B = 1

C = 13

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Let's check the answer. Plug in (x,y) = (2,5) to find that...

4x+y = 13

4*2 + 5 = 13

8 + 5 = 13

13 = 13

We get the same thing on both sides, so the last equation is true. This means the first equation is true when (x,y) = (2,5). This confirms the point (2,5) is on the line and helps confirm the answer.

Answer 2

2x + 5y = -4

Step-by-step explanation:

The standard form for linear equations in two variables is Ax+By=C. For example, 2x+3y=5 is a linear equation in standard form. When an equation is given in this form, it's pretty easy to find both intercepts (x and y). This form is also very useful when solving systems of two linear equations.