Jose is driving to Denver. Suppose that the remaining distance to drive (in miles) is a linear function of his driving time (in
minutes). When graphed, the function gives a line with a slope of -0.95. See the figure below.
Jose has 48 miles remaining after 50 minutes of driving. How many miles were remaining after 34 minutes of driving?

  63.2 miles

Step-by-step explanation:

The given slope and point can let us use the point-slope form of the equation for a line:

  y = m(x -x1) +y1

  y = -0.95(x -50) +48

We want to find the value of y for x=34.

  y = -0.95(34 -50) +48 = 63.2

Jose had 63.2 miles remaining after driving 34 minutes.

(0,-3) see attached graph

step-by-step explanation:

a. to solve the system, graph the two equations.

x = y+3 becomes y=x-3 has m=1/1 and b=-3. start at (0,-3) on the y-axis and plot a point. then move up 1 unit and 1 unit to the right. plot a point and connect.

y=-4x+3 has m =-4/1 and b=-3. start at (0,-3) on the y-axis and plot a point. then move down four units and to the right 1 unit. plot a point and connect.

the solution is the point (x,y) where the two lines intersect. by the graph below it is (0,-3).

b. to solve by substitution, substitute y = -4x-3 into x= y+3

x= (-4x-3) +3

x=-4x

5x=0

x=0

now substitute x = 0 back in to find y.

y= -4(0)-3

y=0-3

y=-3

solution is (0,-3)

c. use elimination by adding the equations together.

x-y=3

4x+y=-3

5x=0

x=0

then substitute into one equation to find y.

y=-4(0)-3

y=-3