Question

What is the equation of the following line? Be sure to scroll down first to see all answer options.

Answer 1

Answer:

y=1/3x

Step-by-step explanation:

change in y/ change in x

2-0/6-0= 2/6=1/3

since its a positive slope, it’s 1/3

Answer 2

Answer:

E. $y=\frac{1}{3}x$

Step-by-step explanation:

Take the two points shown:

$(0,0)(6,2)$

Use these to make an equation in slope-intercept form:

$y=mx+b$

m is the slope and b is the y-intercept (where x is equal to 0).

Use the slope formula:

$\frac{y_{2}-y_{1}}{x_{2}-x_{1}} =\frac{rise}{run}$

Rise over run is the change in the y-axis over the change in the x-axis, otherwise known as the slope. Insert coordinate points:

$(0_{x1},0_{y1})\\\\(6_{x2},2_{y2})\\\\\frac{2-0}{6-0}$

Simplify:

$\frac{2-0}{6-0} =\frac{2}{6} =\frac{1}{3}$

The slope is $\frac{1}{3}$. Insert this into the equation:

$y=\frac{1}{3}x+b$

Now find the y-intercept. Take one of the coordinate points and insert:

$(6_{x},2_{y})\\\\2=\frac{1}{3}(6)+b$

Solve for b. Simplify multiplication:

$\frac{1}{3}*\frac{6}{1}=\frac{6}{3}=2\\\\ 2=2+b$

Use reverse operations to isolate the variable:

$2-2=2-2+b\\\\0=b$

The y-intercept is equal to 0. Insert this into the equation:

$y=\frac{1}{3}x+0$

or

$y=\frac{1}{3}x$

:Done