Question

Write the equation of the line that passes through the points (1,-4) and (5,-1). put your answer in fully simplified point slope form unless it is a vertical or hot line

Answer 1

The equation of the line passing through the points (1, -4) and (5, -1) is found by first calculating the slope, which is 0.75, and then using point-slope form. The final equation in point-slope form is y + 4 = 0.75x - 0.75.

Step-by-step explanation:

The student is asking for the equation of the line that goes through the points (1, -4) and (5, -1). To find the equation of the line, we must first calculate the slope and then use one of the points to find the equation in point-slope form.

The slope (m) can be found using the formula:

m = (y2 - y1) / (x2 - x1)

Using the provided points (1, -4) (x1, y1) and (5, -1) (x2, y2), we get:

m = (-1 - (-4)) / (5 - 1)

m = (3) / (4)

m = 0.75

Now, using the slope and one of the points, for example, point (1, -4), the point-slope form of the line's equation is:

y - (-4) = 0.75(x - 1)

Simplified,

y + 4 = 0.75x - 0.75

This is the fully simplified point-slope form of the line's equation.