Derive the equation of the line in slope-intercept form.

Question

(1 point)

(0,4) and (1,8)

Answer 1

The slope-intercept form of a linear equation is given by y = mx + b, where m is the slope of the line and b is the y-intercept.

To find the slope of the line passing through (0,4) and (1,8), we can use the formula:

m = (y2 - y1) / (x2 - x1)

Plugging in the values from the given points:

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

m = 4 / 1

m = 4

So, the slope of the line is 4.

Now, we can substitute the value of m into the slope-intercept form equation:

y = 4x + b

To find the value of b, we can choose either of the given points. Let's use (0,4):

4 = 4(0) + b

4 = 0 + b

b = 4

So, the equation of the line in slope-intercept form is:

y = 4x + 4.