the slope intercept form of the equation of a straight line is:
y = mx + b
m is the slope
b is the y-intercept.
the slope is found by the formula -m = (y2 - y1) / (x2 - x1)
(x1,y1) are one coordinate point on the line.
(x2,y2) are another coordinate point on the line.
once you find the slope, you can find the y-intercept by using one of the coordinate points and the slope.
an example:
your coordinate points are (3,5) and (6,10)
assign one of the points to (x1,y1) and the other to (x2,y2)
i assigned (3,5) to (x1,y1) and (6,10) to (x2,y2)
the slope is (y2 - y1) / (x2 - x1) which is equal to (10 - 5) / (6 - 3) which is equal to 5/3
now that you know the slope you can solve for the y-intercept.
the equation of y = mx + b become y = 5/3 * x + b
assign one of the coordinate points to x and y.
i chose (6,10).
the equation of y = 5/3 * x + b becomes 10 = 5/3 * 6 + b
simplify to get 10 = 30/3 + b
subtract 30/3 from both sides of the equation to get:
10 - 30/3 = b
solve for b to get b = 30/3 - 30/3 = 0.
the equation becomes y = 5/3 * x + 0 which becomes y = 5/3 * x.
the y-intercept is the value of y when the value of x is equal to 0.
to see if your two points are on the equation, graph the equation.
the graph looks like this:
the red line is the graph of the equation y = 3/5 * x
the blue lines are just there to allow me to show you that the coordinate points used to create the line are on the line.
they're at (3,5) and (6,10, as they should be.
the y-intercept is at (0,0).
that's the value of y when the value of x is equal to 0.