How do you find another point on each line using slope and point given m=3; passes through (-2,4)?

Question

Nathan Axel · Accepted Answer

See below.

We will look at the definition of slope in order to solve this problem. Slope is defined as: #"Slope"=("change in "y)/("change in "x) = ("rise")/("run")# Therefore, if we are given a slope of #3#, we can assume that it means a change in #y# of #3# for every change in #x# of #1#. So, if we want to find another point on the line that #(2,-4)# makes with a slope of #3#, then we can simply add #1# to the #x#, and #3# to the #y#: #(2,-4)# #(2 + 1, -4 + 3)# #(3, -1)# I hope that was helpful.

Hazel Anglin · Answer

undefined To find another point on the line using the slope (m) and a given point (-2,4), you can use the point-slope form of the equation of a line:

y - y1 = m(x - x1)

Substitute the given values into the equation:

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

Simplify:

y - 4 = 3(x + 2)

Distribute 3:

y - 4 = 3x + 6

Add 4 to both sides:

y = 3x + 10

Now, you can choose any value for x and calculate the corresponding y-coordinate using this equation. For example, let's choose x = 0:

y = 3(0) + 10
y = 0 + 10
y = 10

So, when x = 0, y = 10. Therefore, another point on the line is (0, 10).