A triangle has vertices A (1,1) B (2,4) and C (4,2). Line p is parallel to side AB and contains point C. Write an equation for line p. Part 1. Find the slope of AB. Show your work. Part 2. Use the slope from Part 1 and point C to write an equation for line p in slope-intercept form. Show your work.

The equation of line p parallel to side AB and contains point C is y - 2 = 3(x - 4) . The slope of side AB is 3 . The equation for line p in slope-intercept form is y = 3x - 10.

What is slope-intercept form of equation of straight line ?

The equation of a straight line in the form y = mx + c where m is the slope of the line and c is its y-intercept is known as the slope-intercept form. Here both the slope (m) and y-intercept (c) have real values. It is known as slope-intercept form as it gives the definition of both the slope and y-intercept.

How to find the slope of a straight line using two given coordinates ?

Slope of a straight line can be found using two given points say (x1,y1) and (x2,y2).

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

Solving the given question for equation of straight line -

It is given that a triangle has vertices A (1,1), B (2,4) and C (4,2).

Also line p is parallel to side AB and contains point C.

Slope of line p will be same as the slope of side AB as both the lines are parallel and are equally inclined.

Slope of line p (m) = (y2 - y1)/(x2 - x1) where x1 = 1 , x2 = 2 , y1 = 1 and y2 = 4.

m = (4 - 1)/(2 - 1) = 3

Slope of AB = Slope of line p = 3.

Equation of a straight line is → y - y' = m(x - x') where (x',y') is the point through which the line passes.

As the line p passes through point C, x' = 4 and y' = 2 .

Equation of line p is

y - 2 = 3(x - 4).

Solving the given equation to find the slope-intercept form -

⇒ y - 2 = 3x - 12

∴ y = 3x - 10

Which is the required equation of line p in slope-intercept form.

To learn more about equation of straight line, refer -

https://brainly.com/question/16934180

#SPJ2