Question

Derive the equation of the line in slope intercept form (0,4), (1,8)

Answer 1

To derive the equation of the line in slope-intercept form, we need to find the slope of the line (m) and the y-intercept (b).

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

Given points:
(x1, y1) = (0, 4)
(x2, y2) = (1, 8)

Applying the slope formula:
m = (8 - 4) / (1 - 0)
m = 4 / 1
m = 4

Therefore, the slope of the line is 4.

Now, let's substitute one of the points (1, 8) into the slope-intercept form equation: y = mx + b.

8 = 4(1) + b

Simplifying:
8 = 4 + b

To find the value of b, we subtract 4 from both sides of the equation:
8 - 4 = b
4 = b

Therefore, the y-intercept (b) is 4.

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