How do you find the slope given A(2, -4) and B(4, 7)?

Question

Savannah Anderson · Accepted Answer

Slope = #11/2#

A line's gradient, steepness, or slope is described as follows:

The #"the vertical change"/"the horizontal change"# which is written as

#(Delta y)/(Delta x) = "change in y"/"change in x"#

The following formula can be used to determine the slope of a line connecting any two points on a line:

#m = (y_2-y_1)/(x_2-x_1)" "# Either point can be #(x_1, y_1)#

We have #A(2,-4) and B(4,7)#

#m = (7-(-4))/(4-2) = (7+4)/2 = 11/2#

This slope represents a very steep line with a vertical increase of 11 for a mere horizontal change of 2. It is left in this form.

The following graph displays the line with the given slope through the given points: graph{y = 11/2x -15 [-44.56, 115.54, -32.3, 47.7]}

Kennedy Adams · Answer

#+11/2#

#color(blue)("Preamble")#

The slop (gradient) is the amount up or down for a given amount of along reading left to right on the x-axis.

If the slop is like going up a hill then it is positive. On the other hand if it is like going down a hill then it is negative.
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#color(blue)("Answering the question")#

Looking at the x's; the left most point is A as 2 is less than 4.
So we read from point A to point B

Let point 1 be #P_1->(x_1,y_1)=(2,-4)->A#
Let point 2 be #P_2->(x_2,y_2)=(4,7)->B#

The gradient #m->("change in y")/("change in x")->(y_2-y_1)/(x_2-x_1)#

Some people write this as #(Deltay)/(Deltax) = m# where

#Deltay# means change in #y# and #Deltax# means change in #x#

#color(brown)("So we have:")#

#"gradient "->m=(y_2-y_1)/(x_2-x_1)=(7-(-4))/(4-2)=+11/2#

As positive it means the 'slope' is upwards reading left to right.

Isaiah Anthony · Answer

undefined To find the slope given points $A(2, -4)$ and $B(4, 7)$, use the formula for slope: $m = \frac{y_2 - y_1}{x_2 - x_1}$. Substitute the coordinates of the points into the formula: $m = \frac{7 - (-4)}{4 - 2}$. Simplify to get $m = \frac{11}{2}$.