Question

Write the slope-intercept form (y=mx+b) of the equation of the line through the given points.

through:
(0,3)(−4,5)

Answer 1

y=-
`(1)/(2)`+3

Explanation:

To write the equation of the line in slope-intercept form, first calculate the slope of the line (m)

m=
`(y_(2)-y_(1) )/(x_(2) -x_(1) )`

=
`(5-3)/(-4-0)`

=2/-4

=-
`(1)/(2)`

next, calculate b by substituting a point (0, 3) into the equation

y=mx+b

3=(-1/2)(0)+b

b=3

final equation of line is: y=-
`(1)/(2)`+3

Answer 2

Explanation:

General line equation: y = mx + c

When x = 0, y = 3. => (3) = m(0) + c, c = 3.

When x = -4, y = 5. => (5) = m(-4) + c,

5 = -4m + (3), -4m = 2, m = -0.5.

Hence the answer is y = -0.5x + 3.