Question

Use the point-slope form to find the equation of a line with the properties given. Then write the equation in slope-intercept form. Through (2,-6) and (4,-3) The equation of the line is

Answer 1

• y +6 = (3/2)(x -2) . . . . . . point-slope form
• y = (3/2)x -9 . . . . . . . . . . slope-intercept form

Explanation:

You know the slope is given by ...

m = (y2 -y1)/(x2 -x1)

= (-3-(-6))/(4 -2) = 3/2

The point-slope form of the equation of a line through (h, k) with slope m is ...

y -k = m(x -h)

Filling in the values m=3/2, (h, k) = 2, -6), we find the point-slope equation to be ...

y -(-6) = (3/2)(x -2) . . . . point-slope form

Subtracting 6 and eliminating parentheses gives ...

y = (3/2)x -3 -6

y = (3/2)x -9 . . . . . slope-intercept form