Question

Is the point (20 13) on this line? Explain your reasoning.

Answer 1

In order to determine if the point (20,13) is on the line, it is necessary to write the equation of the line.

The general form of a linear equation is:

y = mx + b

where b is the y-intercept and m is the slope. Y-intercept is the value of y when x = 0. You can observe in the graph that b = 3.

The slope m is conputed by using the following formula:

$m=\frac{y_2-y_1}{x_2-x_1}$

where (x1,y1) and (x2,y2) are two points of the line. Use the points (0,3) and (6,6), you can select any other two points. Replace these values into the formula for m:

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

Then, the equation of the line is:

$y=\frac{1}{2}x+3$

Now, replace the value of x = 20 in the previous equation, if y = 13, then the point (20,13) in on the line:

$\begin{gathered} y=\frac{1}{2}(20)+3 \\ y=10+3 \\ y=13 \end{gathered}$

Hence, the point (20,13) is on the line