Question

Graph the line containing the points (5,2) and (0,7) on the coordinate plane below. Then use the graph to determine
the equation of the line.
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Answer 1

Answer:

Part 1) The graph in the attached figure

Part 2) The equation of the line is $y=-x+7$

Step-by-step explanation:

Part 1) we know that

To graph a line we need at least two points

we have

(5,2) and (0,7)

Plot the points

Connect then and join to graph the line

The graph in the attached figure

Part 2) Determine the equation of the line

Find the slope

Remember that the formula of slope is "rise over run", where the "rise" (means change in y, up or down) and the "run" (means change in x, left or right)

see the graph

The formula to calculate the slope between two points is equal to

$m=\frac{rise}{run}$

we have

$rise=-5\\run=5$

substitute

$m=\frac{-5}{5}$

$m=-1$

Is negative because is a a decreasing function

as the value of x increases, the value of y decreases

The equation of the line in slope intercept form is equal to

$y=mx+b$

we have

$m=-1$

$b=7$ ----> the y-intercept is given see the graph

substitute

$y=-x+7$