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.
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:
- the line has a slope, m, of -2/3
- 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