The equation of the line through the points (-5,2) and (0,3) is y = (1/5) * x + 3
The equation of the line through the points (-5,2) and (0,3) can be found using the slope-intercept form of a line, which is:
y = mx + b
where m is the slope of the line and b is the y-intercept, or the point where the line crosses the y-axis.
To find the equation of the line through the points (-5,2) and (0,3), we need to first calculate the slope of the line using the formula:
m = (y2 - y1) / (x2 - x1)
Plugging in the coordinates of the points (-5,2) and (0,3) gives us:
m = (3 - 2) / (0 - (-5)) = 1 / 5
Next, we need to find the y-intercept of the line. We can do this by plugging the slope (m) and one of the points (-5,2) into the slope-intercept form of a line:
y = mx + b
= (1/5) * (-5) + b
= -1 + b
= 2
Solving for b gives us:
b = 2 + 1 = 3
So, the y-intercept of the line is (0,3).
Finally, we can plug the slope (m) and y-intercept (b) into the slope-intercept form of a line to get the equation of the line through the points (-5,2) and (0,3):
y = (1/5) * x + 3
This is the answer to the question.