find the point of intersection of the line passing through two points (3,0) and (0,2) and the line passing through point (-2,10 with slope -3
First, let's find the equation of the line passing through the points (3,0) and (0,2).
The slope (m) of the line passing through the points (x1, y1) and (x2, y2) is given by the formula:
m = (y2 - y1) / (x2 - x1)
Using the points (3,0) and (0,2):
m = (2 - 0) / (0 - 3) = -2/3
Now we have the slope (-2/3) and a point (3,0). We can use the point-slope form of the equation of a line to find the equation of the line passing through these points:
y - y1 = m(x - x1)
y - 0 = (-2/3)(x - 3)
y = -2x/3 + 2
Now, let's find the equation of the line passing through the point (-2,10) with slope -3. The equation of the line in point-slope form is:
y - y1 = m(x - x1)
y - 10 = -3(x + 2)
y - 10 = -3x - 6
y = -3x + 4
Now, we can find the point of intersection of these two lines by setting the two equations equal to each other:
-2x/3 + 2 = -3x + 4
-2x + 6 = -9x + 12
7x = 6
x = 6/7
Now we can substitute the value of x back into either of the equations to find the corresponding y-coordinate. Let's use the first equation:
y = -2(6/7)/3 + 2
y = -4/7 + 2
y = 10/7
Therefore, the point of intersection of the two lines is (6/7, 10/7).