Sonja plays tennis and started a tournament with 43 aces on the season. the graph relates her total season aces with the number of matches played in the tournament.

The first thing we need to do is find the slope of our line. To do it we are using the slope formula:

where

is the slope of the line

are the coordinates of the first point on the line

are the coordinates of the second point

From our graph we can get the points (0, 43) and (2, 55), so , , , and . Let's replace the values in our slope formula:

Now that we have our slope, we can use the point-slope formula:

But remember that the equation of a line in standard form is , so we need to subtract and add 43 to both sides of our point slope equation:

We can conclude that the equation in standard form that represent the relationship in the graph is .

the system of inequity is

step-by-step explanation:

from the given graph it is noticed that we have two related lines. one is solid and another is dashed.

if a line passing through two points, then the equation of line is

the solid line passing through the points (0,4) and (4,0).

the related equation of solid line is .

similarly, find the related equation of dashed line. the dashed liune passing through the points (0,0) and (3,1).

the related equation of dashed line is

from the given graph it is noticed that the point (0,1) lies on the shaded region, therefore the point (0,1) must be satisfied by the related equations.

check the related equations by the point (0,1).

this statement is true if the sign of inequality is < instead of equality. since it is an solid line therefore the sign of inequality will be . the required inequality is

similarly, check the second related equation.

it is a dashed line, so this statement is true if the sign of inequality is > . the required inequality is