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

Question

(the points marked:)
(1,8) (0,4)

Answer 1

First, we need to find the slope of the line using the two points given. The slope formula is

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 the equation of the line:

y - y1 = m(x - x1)

Substitute one of the points into the equation (let's use the point (1, 8)):

y - 8 = 4(x - 1)

Now, simplify and rewrite in slope-intercept form (y = mx + b):

y - 8 = 4x - 4
y = 4x + 4

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

Answer 2

That was wrong

Answer 3

I apologize for the mistake. Let's try again.

Given points: (1, 8) (0, 4)

First, calculate the slope using the formula:

m = (y2 - y1) / (x2 - x1)
m = (8 - 4) / (1 - 0)
m = 4 / 1
m = 4

Now, we have the slope (m = 4), let's use the point-slope form of the equation of a line:

y - y1 = m(x - x1)

Choose one of the points, (1, 8) or (0, 4), let's use the point (0, 4):

y - 4 = 4(x - 0)

y - 4 = 4x

Now, rewrite the equation in slope-intercept form (y = mx + b):

y = 4x + 4

Therefore, the equation of the line in slope-intercept form is y = 4x + 4. This time, the calculation is correct. Thank you for pointing that out.