Which is steeper a hill that rises 2 feet for every 10 feet of run, or a hill that rises 2 feet for every 15 feet of run? explain

Ok, the first hill rises 2 feet for every 10 feet of run.

So if both hills start in the ground where y = 0, we can write the height as a function of x in the next way: y = (2/10)*X so for every 10 feet you advance in x, you rise 2 feet in Y, where here 2/10 is the slope.

The second hill is described by y = (2/15)*X, so for every 15 feet in x, you rise 2 feet in y, and the slope is 2/15

Is easy to see that 2/10 > 2/15, so the slope of the first hill is bigger than the slope of the second hill, this means that the first hill is steeper than the second.

expression #3 is not equivalent. the others are.

step-by-step explanation:

we are given a graph for system of inequalities.

in order to write the system of inequalities for the given graph, we need to find the inequality for each of the line separately.

let us find the slope of dotted line first.

taking two coordinates on the graph.

let us say (0,0) and (3,1).

let us find the slope of the line now.

slope of the dotted line would be =.

y-intercept of dotted line is y=0 only.

plugging slope m= and b=0 in slope-intercept form y=mx+b, we get

.

the line is shaded up of that dotted line.

therefore, for shading up we would take greater than inequality symbol > .

and because it's a dotted line we would take only > symbol in place of = sign in above equation of line.

therefore, inequality for dotted line would be

let us take two points (3,1) and (0,4) on the solid line.

slope of the solid line would be =.

for the solid line we have y-intercept b= 4.

plugging slope m= -1 and b=4 in slope-intercept form y=mx+b, we get

y = -1x + 4.

the line is shaded down of that solid line.

therefore, for shading down we would take less than inequality symbol < .

and because it's a solid line we would take ≤ symbol in place of = sign in above equation of line.

therefore, inequality for solid line would be