Question

Graph the line y-3 =4(x-5)

Answer 1

Here is the graph :)

Answer 2

you need to have the equation look like y=mx+b where m is a number that is your slope and b is another number that is your y-intercept.

I will do this now below:

$y-3=4(x-5)$

Factor 4 into (x-5) because you should always try to expand everything out as much as possible to be able to simplify things later:

$y-3=4(x-5)\\y-3=4x-20$

Now we should try to get y by itself since in y=mx+b format y is by itself.

$y-3=4x-20\\\text{add three to both sides}\\y-3+3=4x-20+3\\y=4x-17$

this is looking like point slope form now, compare the two below:

$y=mx+b\\y=4x-17\\\text{ The m is represented by the 4, x is x, and -17 is the +b}$

Now we need to graph our line. For this part we just pick some numbers for x and put it in the equation and solve for y. This will give us a list of x and y points.

y=4x-17

X$\left[\begin{array}{ccc}x&y(x)&y\\1&4(1)-17&=-13\\2&4(2)-17&=-9\\3&4(3)-17&=-5\\4&4(4)-17&=-1\\5&4(5)-17&=3\end{array}\right]$

So now we have some points and we can put them on a graph:

(1,-13)

(2,-9)

(3,-5)

(4,-1)

(5,3)

Ill attach a picture of the graph below.

And thats the answer, let me know if you have questions.