For what value of b do the lines bx+3y=10 and x–2y=4 intersect at a point on the x-axis?

Since we need to find the point at which the 2 lines intersect at the x-axis, we need to find where the 2nd line intersects the x axis, by plugging in y=0.

x-2(0)=4
x=4
Therefore, at (4,0).

Now we plug in (4,0) at the first equation.
4b+3(0)=10
4b=10
b=5/2

Therefore, at b=5/2

Where m is the slope of the line and b is the y-intercept of the line, or the y-coordinate of the point at which the line crosses the y-axis. to write an equation in slope-intercept form, given a graph of that equation, pick two points on the line and use them to find the slope. this is the value of m in the equation.