Question

Write an equation that represents the situation

Answer 1

Answer:

y = x - 3

Step-by-step explanation:

Given line passes through the points $(3,\:0)=(x_1,\:y_1) \:\&\:(6,\:3)=(x_2,\:y_2)$

Equation of line in two point form is given as:

$\frac{y - y_1}{y_1 - y_2} = \frac{x - x_1}{x_1 - x_2} \\ \\ \therefore \: \frac{y - 0}{0 - 3} = \frac{x - 3}{3 - 6} \\ \\ \therefore \: \frac{y }{- 3} = \frac{x - 3}{ - 3} \\ \huge \red{ \boxed{\therefore \: y = x - 3}} \\ \implies \: y = mx + b$

Answer 2

Answer: y = 1x - 3

Step-by-step explanation:

1. The equation to find slope is shown by the following:

$\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$ = slope                    (another term for slope is "m")

Choose two coordinates on the graph to solve this problem.

I chose (15,12) and (9,6), although any other set of points would have worked

At this point, you would plug the x and y coordinates in their respective places and solve:

$\frac{12-6}{15-9\\}$ = $\frac{6}{6}$ = 1

Now we know the slope/m = 1

This is the equation so far: y = 1x+b

2: Now, we have to solve for b, or the y-intercept

To solve for b, we need to plug in an "(x,y)" coordinate into this equation:

$(y-y_{1}) = m(x-x_{1})$

Choose any coordinate from the graph. In this instance, i chose "(3,0)," but any other point would work.

(y-0) = 1(x-3) --> y = 1x - 3

The equation that represents the line is y = 1x - 3