Question

Instructions: Write the equation of the line passing through the points (-2,3) and (-1, -2) in Slope-Intercept and Point- Slope Form. Slope Intercept Form: Point-Slope Form:

Answer 1

Equation of a Line

The equation of the line in slope-intercept form is:

y=mx+b

Where:

m = slope

b = y-intercept.

The point-slope form of the equation of a line is:

y - k = m ( x - h )

Where m is the slope and (h,k) is a point through which the line passes.

Suppose we know the line passes through points A(x1,y1) and B(x2,y2). The slope can be calculated with the equation:

`\displaystyle m=(y_2-y_1)/(x_2-x_1)`

The line passes through the points (-2,3) and (-1,-2). Calculating the slope:

`\displaystyle m=(-2-3)/(-1+2)=-5`

To write the point-slope form of the line, we use one of the points (-2,3) and the slope:

y - 3 = -5(x + 2)

It can also be written by using the other point (-1,-2):

y + 2 = -5(x + 1)

Operating the parentheses in the first equation:

y - 3 = -5x - 10

Adding 3:

y = -5x - 7

This is the slope-intercept form of the line

It can be found by operating the parentheses on the second equation

Point-Slope form:

y - 3 = -5(x + 2)

y + 2 = -5(x + 1)

Slope-Intercept form:

y = -5x - 7