Question

which equation is in slope-intercept form and represents a line with the slope 1/4 through the point of (0,0)

Answer 1

Hi there!

The general form of the equation of a line in slope-intercept form is
y = ax + b

With 'a' representing the slope of the line. We know that the slope of this line is 1/4, so we can plug in this value into the equation of the line.

y = 1/4 x + b
When the line passes through the point (0,0) we can also plug in the x- and y-coordinate into the equation, and we'll see that some easy algebra will help us find our solution.

0 = (1/4) * 0 + b 
First switch sides

(1/4) * 0 + b = 0
Multiply

0 + b = 0
b = 0

Now we've found our value of 'b', which we can plug back into the equation in slope-intercept form to find our final solution.
y = 1/4 x 
or
f(x) = 1/4 x

~ Hope this helps you!