Finding the Equation for a Line: y=mx+b

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In summary, the equation for a line is y = mx + b, where m is the slope and b is the y-intercept. The slope can be found by using the formula m = (y2-y1)/(x2-x1) or by determining the change in y over the change in x. The y-intercept, represented by b, is the initial value of y when x is 0 and can be found by plotting the point where the line crosses the y-axis. A line can have a slope of 0, meaning it is horizontal with no change in y for any change in x. To graph a line using the equation y=mx+b, plot the y-intercept on the y-axis and use the slope
  • #1
BeachofBrasil
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Find an equation y=mx+b for the line whose graph is sketched.
The number m =
The number b =
 

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  • #2
If y= mx+ b, then y(0)= m(0)+ b= b. That is, b is the y value where x= 0- where the line crosses the y-axis. what is that?

If y(0)= m(0)+ b= b, and y(1)= m(1)+ b= m+ b, then m= (m+b)- b= y(1)- y(0). What is that?
 
  • #3
m=5/6
b=5
 
  • #4
BeachofBrasil said:
m=5/6
b=5
Yes.
 

FAQ: Finding the Equation for a Line: y=mx+b

What is the equation for a line?

The equation for a line is y = mx + b, where m is the slope of the line and b is the y-intercept.

How do you find the slope of a line?

The slope of a line is determined by the change in y over the change in x, or "rise over run". It can also be found by using the formula m = (y2-y1)/(x2-x1), where (x1,y1) and (x2,y2) are two points on the line.

What is the significance of the y-intercept in a line?

The y-intercept, represented by b in the equation, is the point where the line crosses the y-axis. It tells us the initial value of y when x is equal to 0.

Can a line have a slope of 0?

Yes, a line can have a slope of 0. This means that the line is horizontal and has no change in y for any change in x.

How do you graph a line using the equation y=mx+b?

To graph a line using the equation y=mx+b, plot the y-intercept (b) on the y-axis and then use the slope (m) to find at least one more point on the line. Plot that point and then draw a straight line through both points to graph the line.

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