How do you find the slope given #5y - 2x = -3#?

Question

Isaiah Anthony · Accepted Answer

#m=2/5# Given the equation of a line, all we need to do is rearrange it into terms of #y=mx+b# #5y-2x=-3# #5y=2x-3# Add -2x to both sides to get #y# by itself #y=2/5x-3/5# Divide all terms by 5 Now that the equation is in terms of slope-intercept, with the slope being #m# in #y=mx+b#, you can find the slope.

Eva Abramson · Answer

See a solution process below:

We can multiply each side of the equation by #color(red)(-1)# to put the equation in Standard Linear Form. The standard form of a linear equation is: #color(red)(A)x + color(blue)(B)y = color(green)(C)# Where, if at all possible, #color(red)(A)#, #color(blue)(B)#, and #color(green)(C)#are integers, and A is non-negative, and, A, B, and C have no common factors other than 1 #color(red)(-1)(5y - 2x) = color(red)(-1) * -3# #(color(red)(-1) xx 5y) - (color(red)(-1) xx 2x) = 3# #-5y - (-2x) = 3# #-5y + 2x = 3# #color(red)(2)x + color(blue)(-5)y = color(green)(3)# The slope of an equation in standard form is: #m = -color(red)(A)/color(blue)(B)# When you substitute, you get: #m = (-color(red)(2))/color(blue)(-5) = 2/5#

Kennedy Adams · Answer

slope=#2/5# So you're going to want to get it into #mx+b=y# form, where #m# is the slope and #b# is the #x# intercept. To rearrange the equation: #5y-2x=-3# add #2x# to each side, which cancels out #-2x# from the left side #5y=-3+2x# now divide each side by #5#, which crosses out the #5# in #5y# #y=(-3+2x)/5# You now have the correct arrangement of the equation and can even flip #-3# and #2x# to match the form of the equation you want it in #y=(2x-3)/5# Now since you have the equation being divided by #5#, you have to divide both #2# and #3# by #5#, making your new equation: #y=(2/5)x-(3/5)# and following the equation we can now see that #m#, which is the slope, is equal to #2/5#.

Nathan Axel · Answer

undefined To find the slope given the equation $5y - 2x = -3$, rearrange it into slope-intercept form $y = mx + b$ where $m$ represents the slope:

$$5y - 2x = -3$$
$$5y = 2x - 3$$
$$y = \frac{2}{5}x - \frac{3}{5}$$

So, the slope of the line is $m = \frac{2}{5}$.