Which is an equation of the line passing through (-2, 3) and perpendicular to the line 5x - y = 12?

An equation of the line passing through (-2, 3) and perpendicular to the line 5x - y = 12 will be:

Step-by-step explanation:

Given the equation

converting the line into the slope-intercept form y = mx+b, where m is the slope

The slope of the line = m = 5

We know that a line perpendicular to another line contains a slope that is the negative reciprocal of the slope of the other line, such as:

Therefore, the slope of new line = – 1/m = -1/5 = -1/5

Using the point-slope form of the line equation

where m is the slope of the line and (x₁, y₁) is the point

substituting the slope of new line = -1/5 and (-2, 3)

Add 3 to both sides

Therefore, an equation of the line passing through (-2, 3) and perpendicular to the line 5x - y = 12 will be: