Final answer:
The equation of the line that passes through points (-1,4) and (-5,-2) is y = 1.5x + 5.5, which is found by calculating the slope and using the point-slope form.
Step-by-step explanation:
To find the equation of the line that passes through the points (-1,4) and (-5,-2), we first need to calculate the slope of the line. The slope (m) can be found by using the formula: m = (y2 - y1) / (x2 - x1),
where (x1, y1) and (x2, y2) are the coordinates of the two points. Substituting the given points into the formula gives:
m = (-2 - 4) / (-5 + 1) = -6 / -4 = 1.5,
Now that we have the slope, we can use the point-slope form of the equation of a line, y - y1 = m(x - x1). Choosing the point (-1,4), the equation becomes: y - 4 = 1.5(x + 1),
Simplifying this gives us the slope-intercept form of the equation: y = 1.5x + 5.5.
This is the equation of the line that passes through the given points.