Question

graphing equations unit 3 lesson 7

use the image to answer the question
(0,4), (1,8)

derive the equation of the line in slope intercept form

Answer 1

To find the equation of the line in slope-intercept form, we need to determine the slope and the y-intercept.

The slope (m) can be found using the formula:
m = (y2 - y1) / (x2 - x1),

where (x1, y1) = (0, 4) and (x2, y2) = (1, 8).

m = (8 - 4) / (1 - 0)
m = 4 / 1
m = 4

Now that we have the slope, we can use the point-slope form of a linear equation:

y - y1 = m(x - x1),

where (x1, y1) = (0, 4).

Plugging in the values:

y - 4 = 4(x - 0)

Simplifying:

y - 4 = 4x

Finally, rearranging the equation to slope-intercept form (y = mx + b):

y = 4x + 4

Therefore, the equation of the line in slope-intercept form is y = 4x + 4.