i am having problems understanding.... i don't know how to put it so i will just put what the problem is

Write the slope-intercept form of an equation of the line that passes through the given point and is parallel to the graph of each equation
13. (2,-7) y= x-2

i know that 2 and -7 is the slope to the line that i have to get the new line to be parallel to it.... if that makes sence... but please help!!!

in the y-intercept slope form

y = mx + b
the slope is m and the y-intercept is b

(2, -7) is a point and tells you nothing about the slope.

so the given line is y = x-2
or y = 1x - 2, so you know the slope must be 1, since the two lines are to be parallel

and the new line must look like
y = 1x + b, where only the y-intercept or the b would have changed
Now we plug in our new point (2,-7)
-7 = 1(2) + b
b = -9

your new equation parallel to the old one is

y = x - 9

ohhhhhh now i see ok can i do one and could you tell me if im right??

will be here for another 15 minutes

(2,-1) y=2x+2

--------------
y=2x+b
-1=2(2)+b
-1=4+-5
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y=2x-5 <--- is this right?

yep. to check, just plug in (2,-1) and see whether it satisfies the equation. Since 2(2)-5 = -1, you're right on.

thank you sooooo much!!!!

To find the equation of a line that is parallel to another line, you need to use the fact that parallel lines have the same slope. In this case, you are given the point (2, -7) and the equation of the line y = x - 2, which has a slope of 1.

To find the equation of the line parallel to y = x - 2, you need to use the slope-intercept form of a linear equation, which is:

y = mx + b

where m represents the slope and b represents the y-intercept.

Since the new line should have the same slope as the given line, the slope of the new line is also 1. So now you have:

y = 1x + b

To determine the value of b, you can substitute the coordinates of the given point (2, -7) into the equation.

-7 = 1(2) + b

Simplifying the equation, you get:

-7 = 2 + b

To solve for b, subtract 2 from both sides of the equation:

-7 - 2 = b

-9 = b

Now you have the value of b, which is -9. Plugging this value into the equation y = 1x + b, you get:

y = x - 9

Therefore, the slope-intercept form of the equation of the line that passes through the point (2, -7) and is parallel to the line y = x - 2 is y = x - 9.