Question

What is the correct equation for the given graph?

Answer 1

For this case we have that by definition, the equation of a line of the slope-intersection form is given by:

$y = mx + b$

Where:

m: It is the slope of the line

b: It is the cut point with the y axis

According to the graph, we have the points:

$(x_ {1}, y_ {1}) :( 2,0)\\(x_ {2}, y_ {2}) :( 0,4)$

We find the slope:

$m = \frac {y_ {2} -y_ {1}} {x_ {2} -x_ {1}} = \frac {4-0} {0-2} = \frac {4} {- 2} = -2$

Thus, the equation is of the form:

$y = -2x + b$

We substitute a point and find b:

$0 = -2 (2) + b\\0 = -4 + b\\b = 4$

Finally we have:

$y = -2x + 4$

Answer:

$y = -2x + 4$