What are slope-intercept and point-slope forms please show examples?

Answer 1

Slope-intercept is: y = mx + c

where m = slope;

and c = intercept.

Example y = 3x + 5

slope = 3

intercept = 5

Point-slope is: y - y0 = m(x - x0)

where m = slope;

point (x0, y0) is a point on the line.

Example y - 8 = 3(x - 1)

slope = 3

point (1, 8) is on the line.

The two are interchangeable:

y - y0 = m(x - x0)

→ y - y0 = mx - mx0

→ y = mx + (y0 - mx0)

Which means that y0 - mx0 = c, the intercept.

Example:

y - 8 = 3(x - 1)

→ y = 3x + (8 - 3×1)

→ y = 3x + 5

→ the two examples above are the same line in different forms.

Answer 2

Slope-intercept:y = mx + b (where "m" is the slope, and "b" is the y-intercept).

Example:

y = 5x - 3 (slope = 5, y-intercept = -3)

Point-slope:

y - y1 = m(x - x1)

or equivalently:

y = m(x - x1) + y1

Where (x1, y1) is the coordinate of the point, and "m" is the slope.