Respuesta :
Both of these are ways to express linear equations.
[tex]y - y_1 = m(x - x_1)[/tex] is the equation for a line with slope m which contains the point [tex](x_1,y_1)[/tex]. This is called point-slope form.
[tex]y = mx + b[/tex] is the equation for a line with slope m and y-intercept b. That is, it contains the point (0, b). This is called slope-intercept form.
Both of these are perfectly valid ways of writing lines, though sometimes one will be easier to use than the other.
Answer:
Hey there!
Both of these can be used to write the equation of the line. However, for the Y-Y1=M(X-X1) equation, we must know one point on the line (X1, Y1) and the slope of the line, while in the Y=MX+B equation, we need to know the slope and the x or y intercept.
For example, we can convert from Y-Y1=M(X-X1) to Y=MX+B
For example, say the point is (2, 3) and the slope is 1
Then, we have Y-3=1(x-2)
This simplifies to Y-3=1x-2
And to Y=X+1
So it is very possible to change from one form to another.
Let me know if you need more help.