Question

derive the equation of the line in slpoe intercept form

Answer 1

The slope-intercept form of a line is given by the equation y = mx + b, where m represents the slope of the line and b represents the y-intercept (the point where the line intersects the y-axis).

To derive the equation of a line in slope-intercept form, you need two pieces of information: the slope of the line and a point that lies on the line. Once you have these, you can plug in the values for the slope and the point into the formula y = mx + b and solve for b.

For example, if the slope of the line is 2 and the line passes through the point (3, 4), you can plug in the values for m, x, and y into the equation:

4 = 2(3) + b

Solving for b, we get:

4 = 6 + b
b = -2

Therefore, the equation of the line in slope-intercept form is:
y = 2x - 2