Question

I have to take a pic of the question

Answer 1

ANSWER

$y=\frac{2}{3}x+\frac{4}{3}$

EXPLANATION

We want to find the equation of the straight line given on the graph.

The general form of a linear equation is given as:

$y=mx+b$

where m = slope; b = y-intercept

To find the slope, we apply the formula for slope:

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

where (x1, y1) and (x2, y2) are two points on the line

Let us pick (1,2) and (4,4)

Therefore, the slope is:

$m=\frac{4-2}{4-1}=\frac{2}{3}$

To find the equation, we now apply the point-slope formula:

$y-y_1=m(x-x_1)$

Therefore, we have that the equation of the line is:

$\begin{gathered} y-2=\frac{2}{3}(x-1) \\ y-2=\frac{2}{3}x-\frac{2}{3} \\ y=\frac{2}{3}x-\frac{2}{3}+2 \\ y=\frac{2}{3}x+\frac{4}{3} \end{gathered}$

That is the equation of the line.