What is the equation of the line that passes through the point 3 4 and has a slope of 2 3

Point Slope Form:

#(y-y_1) = m(x-x_1)#
Where m is the slope of the line #((Delta y) / (Delta x))#, #y_1# is the y coordinate of a point, and #x_1# is the x coordinate of a point.

For a line with slope -3 and point (-2,4), plug -3 in for m, -2 for #x_1#, 4 for #y_1#.
#(y - 4) = -3(x + 2)#

Standard Form:

Ax + By = C

Where A, B, and C are integers. To write an equation in standard form, rewrite the equation in point slope form so that it fits the formula for standard form.
#(y - 4) = -3(x + 2)#
#y - 4 = -3x - 6#
#y + 3x - 4 = - 6#

#y + 3x = - 2#

Dylan B.

asked • 05/24/21

3 Answers By Expert Tutors

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

Michelle P. answered • 05/24/21

A pre-student teacher with a passion for math!

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

Use ;point-slope form

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

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