Answer:
Explanation:
To find the equation of a line that passes through two given points, we can use the point-slope form of the equation of a line. The point-slope form is:
y - y1 = m(x - x1)
where m is the slope of the line, (x1, y1) is a point on the line, and (x, y) are the coordinates of any other point on the line.
To use this formula, we first need to find the slope of the line that passes through the two given points (-4, -2) and (-6, -5). The slope, denoted by m, is given by the formula:
m = (y2 - y1) / (x2 - x1)
where (x1, y1) = (-4, -2) and (x2, y2) = (-6, -5). Substituting these values, we get:
m = (-5 - (-2)) / (-6 - (-4))
= (-5 + 2) / (-6 + 4)
= -3 / -2
= 3/2
So, the slope of the line is 3/2.
Now, we can choose either of the two given points and use it with the slope to write the equation of the line. Let's use the first point, (-4, -2). Substituting the values of x1, y1, and m in the point-slope formula, we get:
y - (-2) = (3/2)(x - (-4))
Simplifying the right side of the equation, we get:
y + 2 = (3/2)(x + 4)
Expanding the right side, we get:
y + 2 = (3/2)x + 6
Subtracting 2 from both sides, we get:
y = (3/2)x + 4
So, the equation of the line that passes through the points (-4, -2) and (-6, -5) is:
y = (3/2)x + 4