To graph a line, first put the equation into slope-intercept form:
. So what can we do with our equation,
, to get it into slope-intercept form? If we divide both sides of the equation by
, we get
. This gives us several pieces of information. Remember that the
constant term, the one without a variable, tells us the y-coordinate of the y-intercept. The y-intercept is where the graph crosses the x-axis. So here, the constant term is 2; so the y-intercept is
(0,2). That is one of the points. Now what does the slope represent? It is rise/run. Here it is -1/3. So from our y-intercept, (0,2), we can go down one unit and to the right 3 units. This new point is
(3,1). From that point we can apply that again: go down 1 and right 3 units to get another point,
(6,0).
Answer:
9, 32 and 36
Step-by-step explanation:
The perimeter of a triangle is the sum of all the sides. Since you know the perimeter and the expressions for each of the sides, you can set up an equation to solve for the variable and find the values of the other sides:
one side: '4 times the shortest side' = 4s
shortest side: 's'
third side: '23 more than the shortest side' = s + 23
perimeter = 77
Equation: 4s + s + (s + 23) = 77
Combine like terms: 6s + 23 = 77
Subtract 23 from both sides: 6s + 23 - 23 = 77 - 23 or 6s = 54
Divide by 6: 6s/6 = 54/6 or s = 9
one side: 4s = 4(9) = 36
shortest side: s = 9
third side: s + 23 = 9 + 23 = 32
Answer:
x=5
Step-by-step explanation:
9+5x=6x+4
-5x -5x
9=1x+4
-4 -4
5÷1=1x÷1
5=x
Elimination Method:
5x - 4y = 6
-5x + 4y = -10
5x - 4y = 6
+ -5x + 4y = -10
————————-
0 = -4
This statement is false, so there is no solution to the system of equations.
Answer:
$32.18
Step-by-step explanation:
It's really just addition. No explanation necessary.
