Question

Which equation represents Grant's path?

Answer 1

Answer:

$y=4-\frac{x}{2}$

Step-by-step explanation:

Find the coordinates of point A and point B

Looking at the graph

we have the points

A(8,0) and B(-4,6)

step 1

Find the slope m

The formula to calculate the slope between two points is equal to

$m=\frac{y2-y1}{x2-x1}$

substitute the values

$m=\frac{6-0}{-4-8}$

$m=\frac{6}{-12}$

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

step 2

Find the equation in point slope form

$y-y1=m(x-x1)$

we have

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

$point\ A(8,0)$

substitute

$y-0=-\frac{1}{2}(x-8)$

Convert to slope intercept form

$y=mx+b$

Distribute in the right side

$y=-\frac{1}{2}x+4$

rewrite

$y=4-\frac{1}{2}x$ -----> $y=4-\frac{x}{2}$

Answer 2

Answer:

The correct option is B) $y=4-\frac{x}{2}$

Step-by-step explanation:

Consider the provided graph.

The coordinates of A is (8,0)

The coordinates of B is (-4,6)

First find the slope of the line by using the formula: $m=\frac{y_2-y_1}{x_2-x_1}$

Substitute the respective values in the above formula.

$m=\frac{6-0}{-4-8}$

$m=\frac{6}{-12}$

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

Hence, the slope is $-\frac{1}{2}$

Now consider the graph, from the graph we know the y intercept of the line is (0,4).

The slope intercept form is: $y=mx+c$

Where, m is the slope of line and c is the y intercept.

Substitute $m=-\frac{1}{2}$ and c=4 in slope intercept formula.

$y=-\frac{1}{2}x+4$

$y=4-\frac{x}{2}$

Hence, the correct option is B) $y=4-\frac{x}{2}$