1,8 0,4

Question

Derive the equation of the line in slope, intercept form

Answer 1

To find the equation of the line in slope-intercept form, we first need to find the slope of the line using the given points (1,8) and (0,4).

The slope (m) of a line passing through two points (x1, y1) and (x2, y2) can be calculated using the formula:
m = (y2 - y1) / (x2 - x1)

Using the points (1,8) and (0,4):
m = (4 - 8) / (0 - 1)
m = -4 / -1
m = 4

Now that we have the slope, we can use it and one of the points to find the y-intercept (b) of the line. The slope-intercept form of a line is given by:
y = mx + b, where m is the slope and b is the y-intercept.

Using the point (1,8) and the slope we found:
8 = 4(1) + b
8 = 4 + b
b = 8 - 4
b = 4

So the equation of the line in slope-intercept form is:
y = 4x + 4