Final answer:
To find the equation of the line passing through (5, -1) and (7, -7), calculate the slope which is -3, then use the point-slope form with one of the points to get y = -3x + 14.
Step-by-step explanation:
Finding the Equation of a Line
To write the equation of a line that passes through the points (5, -1) and (7, -7), we need to first calculate the slope of the line. The slope can be determined from the following formula:
Slope (m)
= Δy / Δx = (y2 - y1) / (x2 - x1)
By substituting the given points into the formula, we get:
Slope (m) = (-7 - (-1)) / (7 - 5) = -6 / 2 = -3
Now that we have the slope, we can use one of the points and the slope to write the equation in point-slope form:
y - y1 = m(x - x1)
Using the point (5, -1), the equation becomes:
y + 1 = -3(x - 5)
Finally, we can convert this to slope-intercept form by simplifying:
y + 1 = -3x + 15
y = -3x + 14
Therefore, the final equation of the line in slope-intercept form is y = -3x + 14.