Line t passes through (4, 5) and is perpendicular to the line shown on the coordinate grid.

a coordinate plane with a line passing through two points at 0 comma 3 and 5 comma 2

what is the equation of line t in standard form?

5x − y = 15
−5x − y = 15
x − 5y = −75
x + 5y = 75

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

Where:

m: It is the slope of the line

b: It is the cut-off point with the y axis

To find the slope of the plotted line, we need two points, according to the image we have:

The slope is:

Therefore, the equation is of the form:

We substitute one of the points and find "b":

Finally, the equation of the graph is:

By definition, if two lines are perpendicular then the product of their slopes is -1. Thus, the slope of a perpendicular line will be:

Thus, the equation of the line t is of the form:

y = 5x + b

We substitute the point and find "b":

Finally, the equation is of the form:

Option A

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step-by-step explanation: