Question

Write an equation of a line that passes through the point (2, 4) and whose slope is 1/2.


y – 2 = 1/2(x – 4)

y – 2 = 4(x – 1/2)

y – 4 = 1/2(x – 2)

y – 4 = 1/2(x +2)

Answer 1

I will adopt a different approach than just telling the formula required.
I had pointed out that the equation of a line with slope m and y-intercept c is given as
y = mx+c
I will use this formula to help solve your question.
What is slope:
Slope is the ratio of change in the y-coordinate with respect to change in the x-coordinate
So, for example,
if slope = 2, then changing the x-coordinate by 1 produces a change in the y-coordinate by 2.

Now here, we are given that the line has a slope of 1/2 and it passes through (2,4)
In order to use the equation y= mx+c,
we need the
1. slope and
2. y-intercept
We already have the slope. All we need to find is the y-intercept.
The y-intercept is the coordinate (0,y) i.e. the point where the line touches the y-axis and for that to happen, the x-coordinate of that point must be zero.
Let us start from the point (2,4)
To go from x = 2 to x = 0, the change in x-coordinate is -2
Now as slope is 1/2, a change of x-coordinate -2 will give a change in y-coordinate od half of -2 i.e. change in y-coordinate = 1/2 * -2 = -1
Thus the y-intercept is 4+(-1) = 3

Thus the equation is y = 0.5x + 3
You can probably see that the third option satisfies this