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How Do You Find the Y-Intercept of a Line If You Have Another Point and the Slope?

What is the y-intercept of the line with slope 1150 that goes through the point (1,1200)?

Summary

  1. The slope-intercept form (y=mx+b) will help us find the y-intercept
  2. m stands for the slope, and b stands for the y-intercept
  3. We know that the slope, m, is equal to 1150
  4. We also know that the line passes through the point (1,1200), which is in the form (x,y)
  5. We can plug the things we know into the equation y=mx+b
  6. Create the final equation by plugging in the slope and y-intercept into y=mx+b
  7. The y-intercept is 50

Notes

    1. There are several different equations for a line, we need to pick the one best suited towards helping us find the y-intercept
    1. We need to pick the equation best suited towards helping us find the y-intercept
    2. An equation with the y-intercept in it would be very helpful
    1. An equation with the y-intercept in it would be very helpful
    1. In order to find the y-intercept using the slope-intercept form we need to know the slope and a point on that line, luckily we have both
    2. m is the slope, which we know is 1150
    3. The point (1,1200) is on our line
    1. We know the slope to be 1150
    2. We can use the slope and the point to find the y-intercept!
    1. 1 is the x-coordinate and 1200 is the y-coordinate in (1,1200)
    1. 1 is the x-coordinate and 1200 is the y-coordinate in the point (1,1200)
    2. We're going to plug the x- and y-values of the point (1,1200) into the x and y of our equation, y=mx+b
    1. 1 is the x-coordinate and 1200 is the y-coordinate in the point (1,1200)
    2. We're going to plug the x- and y-values of the point (1,1200) into the x and y of our equation, y=mx+b
    1. We can plug the slope (m) into our slope-intercept form, which right now looks like 1200=m•1+b
    1. We can solve 1200=1150•1+b for the y-intercept (b)
    1. We can solve 1200=1150•1+b for the y-intercept (b)
    2. 1200=1150•1+b=1150+b
    3. Subtract 1150 from both sides to get b=1200-1150=50
    1. We need to rewrite the slope-intercept form of our line with both the slope (m) and y-intercept (b) plugged in
    2. Slope-intercept form is y=mx+b
    1. We need to rewrite the slope-intercept form of our line with both the slope (m) and y-intercept (b) plugged in
    2. Slope-intercept form is y=mx+b
    3. m=1150 and b=50
    1. The final equation for this line is y=1150x+50