Question

A line goes through the points (5.20) and (0.5).

(a) What is the slope of the line? Show your work

(b) Write the equation of the line in point-slope form. Show your work

(c) Write the equation of the line in slope-intercept form. Show your work.​

Answer 1

`\bold{ANSWER:}`
(a) m = 3
(b) y - 20 = 3x - 15
(c) y = 3x + 5


`\bold{SOLUTIONS:}`

(a) To find the slope of the line passing through the points (5, 20) and (0, 5), we can use the formula:

slope (m) = (y2 − y1) / (x2 − x1)

Let's substitute the given values into the formula:

m = (20 - 5) / (5 - 0)

m = 15/5

m=3

Therefore, the slope of the line is 3.

(b) To write the equation of the line in point-slope form, we can use the formula:

y - y1 = m(x-x1)

Let's substitute one of the given points, (5, 20), into the formula:

y - 20 = 3(x-5)

Simplifying the equation:

y - 20 3x - 15

This is the equation of the line in point-slope form.

(c) To write the equation of the line in slope-intercept form, we need to solve the equation obtained in part (b) for y.

y - 20 = 3x - 15

Adding 20 to both sides of the equation:

y = 3x - 15 + 20

y = 3x + 5

Therefore, the equation of the line in slope-intercept form is y = 3x + 5.