What is the equation of the line that passes through the point (3,4) and has a slope of -2/3 ?

Answer 1

Hi Dylan B.

 

You can use the Slope Intercept Form of a line and the coordinates given to develop your line

Slope Intercept Form is

y = mx + b; where m is the slope

You are given m = -2/3

We can start with

y = (-2/3)x + b

Now use the coordinates given (3,4) to solve for b

y = (-2/3)x + b

4 = (-2/3)*3 + b

4 = -2 + b

4 + 2 = b

and your line is

y = (-2/3)x + 6

I hope this helps

Answer 2

I'm going into this problem assuming that your teacher is asking for slope-intercept form (y = mx + b). If it's something else, feel free to correct me.

You have two useful pieces of info in this problem:

1. the line has a slope, m, of -2/3
2. the line passes through (3,4)

The only missing component is the y-intercept, b. We can plug in what we know into the general slop-intercept form equation to obtain the y-intercept of the line. So we start with

y = mx+b

Plug in m = -2/3, x = 3, and y = 4:

4 = (-2/3)(3) + b

Now we want to get b by itself. Multiply -2/3 and 3:

4 = -2 + b

Add 2 to both sides

6 = b

So the line has a y-intercept of 6. Plug our newfound b value and given m value into y=mx+b, and your final answer is:

y = (-2/3)x + 6

Answer 3

Use ;point-slope form

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