This one is a basic problem with two unknowns in two equations. Derive y=x+10 from the second equation and replace the y in first equation to solve the problem. So, x+10+5x=40 and x = 5. X-y= -10 so y=15. The graph below illustrates the solution.

再一次相同的过程是必需的。这个问题however involved multiplying x by y so is a bit different. We end up with two possible solutions. Derive y=x+1 and solve in the same manner as the ones above. The graph below illustrates the solution.

Similar problem to the one before, with x being divided by y instead of multiplied. Solve in the same manner but keep in mind the way that x/y is graphed. We end up solving for one solution. The graph below illustrates the solution,

Straightforward problem that presents two unknowns with two equations. The student will need to deal with the fractions correctly to get this one right. Other than the fraction the problem is solved in the exact same manner as the rest in this set. The graph below illustrates the solution.

First we need to find the slope. Slope (m) = (y₂- y₁)/(x₂- x₁). Substituting in our values (-5 - 4)/(2 - (-1)) = -9/3 = -3 so slope = -3. The formula for a line is y = mx +b. We know m = -3 so now we can pick one of the two points, substitute in the values for x and y, and find b. 4 = (-3)(-1) + b so b = 1. Our formula is thus y = -3x + 1

We will find the equation using slope intercept form: y=mx+b

1. Use the two points to find the slope.

The equation to find the slope of this line using two points is:

Therefore, m =¹/₂, so the slope of this line is¹/₂.

2.现在我们已经斜率,我们可以使用一个the points that were given to find the y intercept. In order to do this, substitute y for the y value of the point, and substitute x for the x value of the point.

Using the point (–2, –2), we now have: –2 = (¹/₂)(–2) + b.

Simplify the equation to solve for b. b = –1

3. In this line m =¹/₂and b = –1

4. Therefore, y =¹/₂x –1

Let P₁(1, 1) and P₂(–2, 3).

First, find the slope using m = rise ÷ run = (y₂– y₁)/(x₂– x₁) giving m = –2/3.

Second, substutite the slope and a point into the slope-intercept equation y = mx + b and solve for b giving b = 5/3.

Third, convert the slope-intercept form into the standard form giving 2x + 3y = 5.

The answer is 22.5.

From the image we can tell that angle a and angle b are complimentary

a + b = 90 and 3a = b

a + 3a = 90

a = 22.5

In order to find the equation of the line, we need to find two points on the line. We are told that the line passes through they-intercept and onex-intercept ofy= –x²– 2x+ 8.

First, let's find they-intercept, which occurs wherex= 0. We can substitutex= 0 into our equation fory.

y= –(0)²– 2(0) + 8 = 8

The y-intercept occurs at (0,8).

To determine thex-intercepts, we can sety= 0 and solve forx.

0 = –x²– 2x+ 8

–x²– 2x+ 8 = 0

Multiply both sides by –1 to minimize the number of negative coefficients.

x²+ 2x– 8 = 0

We can factor this by thinking of two numbers that multiply to give us –8 and add to give us 2. Those numbers are 4 and –2.

x²+ 2x– 8= (x+ 4)(x– 2) = 0

Set each factor equal to zero.

x+ 4 = 0

Subtract 4.

x= –4

Now setx– 2 = 0. Add 2 to both sides.

x= 2

Thex-intercepts are (–4,0) and (2,0).

However, we don't know whichx-intercept the line passes through. But, we are told that the line has a negative slope. This means it must pass through (2,0).

The line passes through (0,8) and (2,0).

We can use slope-intercept form to write the equation of the line. According to slope-intercept form,y=mx+b, wheremis the slope, andbis they-intercept. We already know thatb= 8, since they-intercept is at (0,8). Now, all we need is the slope, which we can find by using the following formula:

m= (0 – 8)/(2 – 0) = –8/2 = –4

y=mx+b= –4x+ 8

The answer isy= –4x+ 8.

Equation of line:,= slope,=-intercept

Step 1) Find slope (): rise/run

Step 2) Find-intercept ():