Hi, I have to use algebra to find the coordinates of the point where two lines intersect, the first line passes through the points 4,3 and 10,0 and the second line is y=6.

Any ideas would be very much appreciated, many thanks

Y = 6 is a horizontal line. The other one we have to figure out

slope = (0-3)/(10-4) = -3/6 = -1/2
so
y = -x/2 + b
0 = -5+b
b = 5
so
y = -x/2 + 5
where does hat hit y=6?
6 = -x/2 + 5
-x/2 = 1
x = -2
so
(-2,6)

BY the way:

Always sketch a graph.
Then this stuff gets easy.

To find the coordinates of the point where two lines intersect, you need to set the equations of the two lines equal to each other and solve for the variables. In this case, you have one line in the form of two points and another line in the form of an equation.

Let's start by finding the equation of the first line using the two given points (4, 3) and (10, 0). We can use the slope-intercept form of a linear equation, which is y = mx + b, where m is the slope and b is the y-intercept.

First, find the slope (m):
m = (y2 - y1) / (x2 - x1)
= (0 - 3) / (10 - 4)
= -3/6
= -1/2

Now we have the slope (m), and we can find the y-intercept (b) by substituting one of the given points into the equation:
3 = (-1/2)(4) + b
3 = -2 + b
b = 3 + 2
b = 5

So, the equation of the first line becomes: y = (-1/2)x + 5.

Now, to find the intersection point with the second line, which is y = 6, we can substitute this value of y into the equation of the first line and solve for x:
6 = (-1/2)x + 5
1 = (-1/2)x
x = -2

Finally, we substitute the value of x into the equation of the second line to find the corresponding y-coordinate:
y = 6

Therefore, the coordinates of the point where the two lines intersect are (-2, 6).