Question

Write the equation of the line in fully simplified slope-intercept form.

Answer 1

`y = -(1)/(6)x +2`

Explanation:

To write an equation into slope-intercept form, or y = mx + b format, we need to find the y-intercept of the line and its slope and substitute values for m and b.

1) First, find the y-intercept. The y-intercept is the point at which the line intersects the y-axis. Reading the graph, we can see that the line passes the y-axis at the point (0,2), thus that is the y-intercept.

2) Next, find the slope. Pick out two points on the graph to use for the slope formula,
`(y_2-y_1)/(x_2-x_1)`. I chose to work with (0,2) and (6,1). Now, substitute the two points' x and y values into the formula appropriately and solve:

`((1)-(2))/((6)-(0)) \\= (1-2)/(6-0)\\= (-1)/(6)`

Thus,
`-(1)/(6)` is the slope.

3) Now, substitute the calculated values into the y = mx + b format. The b represents y-value of the y-intercept. The y-intercept is (0,2), thus substitute 2 for b. The coefficient of the x term, or m, represents the slope, thus substitute
`-(1)/(6)` for m. This will give the following equation of the line in slope-intercept format:

`y = -(1)/(6)x +2`