how do i write an equation in point-slope form for the line that passes through each point with the given slope

 The basic form for a point-slope equation is

y - b = m(x - a)

a is the x-value from the given coordinate,  b is the y-value form the given coordinate,  m is the slope. x and y are the variables in the function.

Use the coordinates given to calculate the slope, then rewrite the equation with any of the given coordinates.

The attachment shows the graph of this equation

Step-by-step explanation:

For example, Given coordinate points: (4,4) and (5,7)

To find the slope, m, use the given coordinates. Get the difference in the y-values and divide by the difference in the x-values. This is "rise over run."

Substitute values:

m= 7-4/5-4  becomes  m= 3/1   so the slope m = 3

To write the equation:  Take the basic form, substitute b and a values from either given coordinate. And use the value of m we just calculated.

y - b = m(x - a)  Using the second coordinate: (5,7)

y - 7 = 3(x - 5)

Or using the first coordinate it would be

y - 4 = 3(x-4)

The slope intercept form of this equation is

y = 3x - 8