Since the line goes through  we know that  is the y-intercept.  

Since we are looking for parallel lines, we need to write the equation of a line that has the same slope as the original, which is .

Slope-intercept form equation is , where  is the slope and  is the y-intercept.

Therefore,

.

Step 1: Find the Slope

Step 2: Find the y-intercept

Use the slope and a point in the original y-intercept

Step 3: Write your equation

Since we know the slope and we know a point on the line we can use those two piece of information to find the y-intercept.

Slope is the change of a line. To find this line one can remember it as rise over run. This rise over run is really the change in the y direction over the change in the x direction.

Therefore the formula for slope is as follows.

Plugging in our given points 

 and ,

.

To find the equation of this line, first find the slope. Recall that slope is the change in y over the change in x: . Then, pick a point and use the slope to plug into the point-slope formula (): . Distribute and simplify so that you solve for y: .

In  form, where y = maximum heart rate and x = age, we can express the relationship as: 

We are looking for a graph with a slope of -1 and a y-intercept of 220.

The slope is -1 because as you grow one year older, your maximum heart rate decreases by 1.

To solve this, first put the linear equation into slope-intercept form:

.

Recall that in slope intercept form

,

the m term is the slope value.

Therefore, the slope is 2.

The graph of a quadratic function  has an -intercept at any point  at which , so, first, set the quadratic expression equal to 0:

The number of -intercepts of the graph is equal to the number of real zeroes of the above equation, which can be determined by evaluating the discriminant of the equation . Set , and evaluate:

The discriminant is positive, so there are two real solutions to the quadratic equation, and the graph of the function has two -intercepts.

Let's start by looking at the given equation:

The inequality is written in slope-intercept form; therefore, the slope is equal to  and the y-intercept is equal to .

All of the graphs depict a line with slope of  and y-intercept . Next, we need to decide if we should shade above or below the line. To do this, we can determine if the statement is true using the origin . If the origin satisfies the inequality, we will know to shade below the line. Substitute the values into the given equation and solve.

Because this statement is true, the origin must be included in the shaded region, so we shade below the line.

Finally, a statement that is "less than" or "greater than" requires a dashed line in the graph. On the other hand, those that are "greater than or equal to" or "less than or equal to" require a solid line. We will select the graph with shading below a dashed line.

Do the first row first and use x and y to represent your variable.