Answer:
(-3, -2)
Explanation:
To find the value of y so that the line passing through the two given points has a slope of 1, we can use the formula for the slope of a line, which is given by:
m = (y2 - y1) / (x2 - x1)
In this case, we know that the slope of the line is 1, so we can set up the equation:
1 = (y - (-2)) / (-9 - (-3))
Solving for y, we get:
1 = (y + 2) / 6
Therefore, y = 1 * 6 - 2 = 4, so the value of y that we are looking for is 4.
Alternatively, we can use the two given points to write the equation of the line in slope-intercept form, which is given by:
y = mx + b
In this case, we know that the slope of the line is 1, so we can write the equation as:
y = x + b
We also know the coordinates of one of the points on the line, (-3, y), so we can substitute these values into the equation to solve for b:
y = (-3) + b
Substituting the value of y that we found earlier, 4, we get:
4 = (-3) + b
Solving for b, we get:
b = 4 + 3 = 7
Therefore, the equation of the line that passes through the two given points and has a slope of 1 is y = x + 7. This equation is in slope-intercept form, so it shows us the value of y when x is 0, which is 7. Since the y-coordinate of one of the given points is -2, we know that this point must be (-3, -2), and we can verify that this point satisfies the equation y = x + 7.