The slope intercept-form of an equation of a line is y=mx+b

Given that the slope is 3 and a point on the line is P(-2, 4), then

m=3 and from the point (-2, 4), x=-2 and y=4.

Substitute the m, x, and y into the slope intercept form

y=mx+b.

4=3(-2)+b   Now solve for b.

4=-6+b

4+6=b

10=b

Now you know b=10 and you already know the slope m=3. Substitute these values into y=mx+b. When you do you will get y=3x+10. This is your answer in slope intercept form.

Equation of the line having slope 'm' & passing through a point (a,b) is :-

y - b = m(x-a)

The standard for of representing a line in slope-intercept form is :-

y = mx + b ; where m = slope of the line & 'b' = y-intercept

Now, the line passes through the point (-2,4) & has slope 3

Thus,  equation of the line is :-

y - (4) = 3*(x-(-2))

or, y - 4 = 3x + 6

or, y = 3x + 10 = slope-intercept representation of the line

If we know that the slope of our line is 3 and the point that it is passing through is (-2,4), then we can use slope-intercept form to solve it. The formula y=mx+b.  In this formula the m represents the slope, the x and y represent the coordinates of the point, and the b represents the y-intercept (where it crosses the y axis of the graph).  Let's begin by plugging in what we know:

4=3(-2)+b   Our first step is to solve for b so that we can find our intercept.

4= -6+b

+6   +6

-----------

10=b

Once we know what our y-intercept (b) is, we can the go back to our original equation and rewrite it so that it is in slope-intercept form.  In slope-intercept form the values of x and y are left out so that other points along the line can be determined.  Therefore our solution will be y=3x+10