In the graph where the line intercepts is (0,4) and the next point is at (1,8)

Question

Derive the equation of the line in slope-intercept form

Answer 1

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

The slope (m) can be found using the formula: m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are the coordinates of two points on the line.

Using the given points (0,4) and (1,8), we can calculate the slope:
m = (8 - 4) / (1 - 0) = 4 / 1 = 4

Now, we have the slope (m) as 4.
To find the y-intercept (b), we can substitute one of the points (0,4) into the slope-intercept form equation and solve for b.

Using the point (0,4) and the slope (m = 4):
4 = 4(0) + b
4 = 0 + b
b = 4

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

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