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.