Question

write an equation of the line in point slope form that passes through the given points (3,4) and (4,6)An equation of the line is??

Answer 1

re The point-slope form of a line is

$y-y_1=m(x-x_1)$

The slope m of the line passing through these two points is the difference between their y coordinates divided by the difference between their x - coordinate.

$m=\frac{6-4}{4-3}$$m=2$

Now we need only find the y-intercept.

Let us use the point (3, 4) which tells us that at x = 3, y = 4; therefore,

$4-y_1=2(3)$$y_1=-2$

Hence, the question of our line in point-slope form is

$\textcolor{#FF7968}{y+2=2x}$

Alternatively, when we have the slope of the line we would just use one of the points to quickly write the point-intercept form.

The y_1 and x_1 in the very first equation are the coordinates of one of the points on the line =. We know that one of the point on our line is (3, 4);