the line passing through points (-3,1) and (2,4)
To find the equation of the line passing through the points (-3,1) and (2,4), we can use the point-slope form of a line.
The point-slope form of a line is given by:
y - y1 = m(x - x1)
Where (x1, y1) is a point on the line and m is the slope of the line.
First, let's find the slope (m) using the formula:
m = (y2 - y1) / (x2 - x1)
Substituting the coordinates of the two points:
m = (4 - 1) / (2 - (-3))
m = 3 / 5
Now, let's choose one of the points, (-3,1), and substitute it into the point-slope form along with the slope:
y - 1 = (3/5)(x - (-3))
Simplifying:
y - 1 = (3/5)(x + 3)
y - 1 = (3/5)x + 9/5
To get the equation in slope-intercept form (y = mx + b), we can move the -1 term to the right side:
y = (3/5)x + 9/5 + 1
y = (3/5)x + 14/5
Thus, the equation of the line passing through the points (-3,1) and (2,4) is y = (3/5)x + 14/5.