Question

(Score for Question 2: ___ of 5 points)
3. A line goes through the points (3,4) and (-3,6).
(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:

Answer 1

Answer:

Step-by-step explanation:

a) Let's do this question by point-slope form, since we're given two coordinates, It's easier to use this method.

y-$y_{1}$ = m(x-$x_{1}$)

6-4 = m(-3-2)

2=m(-5)

m= -2/5 Answer

b) It's easier since we solved the previous question with point slope form

y-4= -2/5 (x-3) Answer

c) y= mx + b (solve for the y-intercept)

4 = -2/5 (3) + b

4 + 6/5 = b

26/5 = b

Hence the equation is y = -2/5x+26/5 Answer

Hope this helps!

if you need clarifications anywhere, please let me know!

Answer 2

Answer:

Step-by-step explanation:

Let the points be $\left ( x_1,y_1 \right )=\left ( 3,4 \right )\,,\,\left ( x_2,y_2 \right )=\left ( -3,6 \right )$.

(a) Slope of the line = $\frac{y_2-y_1}{x_2-x_1}=\frac{6-4}{-3-3}=\frac{2}{-6}=\frac{-1}{3}$

(b) Let the slope be m.

From part (a), m = $\frac{-1}{3}$

Point slope form is as follows:

$y-y_1=m(x-x_1)\\y-4=\frac{-1}{3}\left ( x-3 \right )$

(c) Slope intercept form is y = mx + b

where m is the slope of line and b is the y-intercept.

Here, m = $\frac{-1}{3}$

To find : b

On putting $\left ( x,y \right )=\left ( 3,4 \right )$, we get

$4=\frac{-1}{3}(3)+b\\4+1=b\\5=b$

So, slope intercept form is $y=\frac{-1}{3}x+5$