www.VirtualNerd.com

How Do You Write an Equation of a Line in Slope-Intercept Form If You Have One Point and a Parallel Line?

Find an equation of the line (in slope-intercept form) that passes through (1,10) and is parallel to the graph of 2x-y = 2

Summary

  1. 'L1' is a variable representing our given line
  2. 'L2' is a variable representing the parallel line we are trying to find
  3. 'y=mx+b' is the form for an equation in slope-intercept form, where 'm' is the slope and 'b' is the intercept
  4. 'y=2x-2' is our given equation in slope-intercept form, where 'm' and 'b' are both '2'
  5. Parallel lines have equal slopes, so 'L2' has a slope of 2
  6. 'y=2x+b' is the half-finished equation for our parallel line
  7. We can solve for 'b' by plugging our point (1,10) into the 'y=2x+b' equation, and we get '8=b'
  8. The final equation for 'L2' is: 'y=2x+8'

Notes

    1. '2x-y=2' is the line we were given, which is in standard form
    1. '2x-y=2' is the line we were given, which is in standard form
    1. Our given line can help us do this
    1. Our given line can provide us with some useful information
    1. '2x-y=2' is the line we were given, which is in standard form
    1. '2x-y=2' is the line we were given, which is in standard form
    2. 'y=mx+b' is the form for an equation in slope-intercept form
    1. '2x-y=2' is the line we were given, which is in standard form
    2. 'y=mx+b' is the form for an equation in slope-intercept form
    1. '2x-y=2' is the line we were given, which is in standard form
    2. 'y=mx+b' is the form for an equation in slope-intercept form
    3. Since we want slope-intercept form, we need to get the y alone on the left
    1. '2x-y=2' is the line we were given, which is in standard form
    2. 'y=mx+b' is the form for an equation in slope-intercept form
    3. Since we want slope-intercept form, we need to get the y alone on the left
    1. '2x-y=2' is the line we were given, which is in standard form
    2. 'y=mx+b' is the form for an equation in slope-intercept form
    3. Since we want slope-intercept form, we need to get the y alone on the left
    4. When we multiply by -1, all signs flip
    1. We use the commutative property to rearrange our equation so that it more closely resembles 'y=mx+b' form
    1. 'y=mx+b' is the form for an equation in slope-intercept form, where 'm' is the slope and 'b' is the intercept
    2. 'y=2x-2' is now our rearranged equation for the given line
    1. Our given line can provide us with some useful information about the parallel line
    1. Our given line can provide us with some useful information about the parallel line
    1. Our given line can provide us with some useful information about the parallel line
    2. We know the slope of our given line, it's 2!
    1. 'y=2x-2' is our rearranged equation for the given line
    2. 'y=mx+b' is the form for an equation in slope-intercept form, where 'm' is the slope and 'b' is the intercept
    1. Remember our trick says that parallel lines have the same slope!
    2. We know the slope of our given line, it's 2!
    1. We want our parallel line to have the 'y=mx+b' form
    2. We can substitute '2' in for 'm' in the 'y=mx+b' equation for our parallel line
    1. In the 'y=mx+b' equation, 'b' is the intercept
    1. We want our parallel line to have the 'y=mx+b' form
    1. We want our parallel line to have the 'y=mx+b' form
    2. The slope of the parallel line is the same as the given line, so it's 2!
    1. We want our parallel line to have the 'y=mx+b' form
    2. The slope of the parallel line is the same as the given line, so it's 2!
    3. So far, our parallel line looks like this: 'y=2x+b'
    1. We want our parallel line to have the 'y=mx+b' form
    2. The slope of the parallel line is the same as the given line, so it's 2!
    3. So far, our parallel line looks like this: 'y=2x+b'
    1. So far, our parallel line looks like this: 'y=2x+b'
    2. Here, 'b' is the y-intercept
    1. So far, our parallel line looks like this: 'y=2x+b'
    2. We want to figure out what the intercept ('b') is
    3. Since we know that the parallel line will "intercept" the point (1,10), this information will help us find 'b'
    1. For the point (1,10), the x-coordinate is '1' and the y-coordinate is '10'
    2. Here, 'b' is the y-intercept
    1. So far, our parallel line looks like this: 'y=2x+b'
    2. Pluggin in '1' for 'x' and '10' for 'y', we get the equation: '10=2•1+b'
    1. Pluggin in '1' for 'x' and '10' for 'y', we get the equation: '10=2•1+b'
    2. Simplifying, the equation becomes: '10=2+b'
    3. Subtracting 2 from both sides gives us: '10-2=2-2+b'
    4. Simplifying again, we get: '8=b'
    1. Remember, we solved for 'b' by just plugging our point (1,10) into the half-finished equation for our parallel line
    2. Here, 'b' is the y-intercept
    1. Up to this point, our parallel line looked like this: 'y=2x+b'
    2. Now we have 'b', which is '8', for our parallel line
    1. So our full equation for the parallel line is: 'y=2x+8'