How do you write the equation in point slope form given (-1,2) and parallel to the line whose equation is 3x-2y=7?

Question

Hazel Anglin · Accepted Answer

#y-2=3/2(x+1)# #"the first thing to know is that"# #• " parallel lines have equal slopes"# #"to obtain the slope rearrange "3x-2y=7# #"into "color(blue)"slope-intercept form"# #•color(white)(x)y=mx+b# #"where m represents the slope and b the y-intercept"# #3x-2y=7# #rArr-2y=-3x+7# #rArry=3/2x-7/2larrcolor(red)" in slope-intercept form"# #rArrm=3/2# #"expressing the equation in "color(blue)"point-slope form"# #•color(white)(x)y=y_1=m(x-x_1)# #"with "m=3/2" and "(x_1,y_1)=(-1,2)# #rArry-2=3/2(x+1)#

Jace Anderson · Answer

undefined To write the equation of a line in point-slope form parallel to the line $3x - 2y = 7$ and passing through the point $(-1, 2)$, we first need to determine the slope of the given line.

Rearranging the equation $3x - 2y = 7$ into slope-intercept form $y = mx + b$, where $m$ is the slope, we have:

$$3x - 2y = 7$$
$$-2y = -3x + 7$$
$$y = \frac{3}{2}x - \frac{7}{2}$$

So, the slope of the given line is $m = \frac{3}{2}$.

Since the line we want to find is parallel to this line, it will have the same slope.

Therefore, the equation of the line in point-slope form is:

$$y - y_1 = m(x - x_1)$$

Substituting the given point $(-1, 2)$ and the slope $m = \frac{3}{2}$ into the equation:

$$y - 2 = \frac{3}{2}(x - (-1))$$
$$y - 2 = \frac{3}{2}(x + 1)$$
$$y - 2 = \frac{3}{2}x + \frac{3}{2}$$

Therefore, the equation of the line in point-slope form parallel to $3x - 2y = 7$ and passing through $(-1, 2)$ is:

$$y - 2 = \frac{3}{2}x + \frac{3}{2}$$