Question

Calculate the slope of the line through the points (6,-8) and (3,-4)

a. Write the equation of the line

b. Is the point (-3,4) on the line you found in part (a)? How can you tell?

Answer 1

a. y=-4/3 x

b. Yes because the point makes the equation true.

Explanation:

To write the equation of a line we must have a slope and a point. To find the slope we use the slope formula and substitute (x,y) points in it as shown below:

`m=(y_2-y_1)/(x_2-x_1)=(-4--8)/(3-6)=(-4+8)/(-3)=(4)/(-3)=(-4)/(3)`

Now that we have the slope, plug in the slope and choose one point to plug into the point slope formula. Use the point-slope form to write the equation, then simplify and convert into the slope intercept form.

(y--4)=-4/3(x-3)

y+4=-4/3(x-3)

y+4=-4/3x +4

y=-4/3x

Test (-3,4): 4= -4/3 (-3)

4=4 Yes