Question

Write an equation that represents the line. (Use exact numbers)

Answer 1

Answer (assuming it can be in slope-intercept form):

`y = (3)/(4) x+2`

Explanation:

When knowing the y-intercept and a slope of a line, you can write its equation in slope-intercept form, or y = mx + b format.

1) First, find the slope. Use two points from the graph. We can see that the points (0,2) and (4,5) are on the line, therefore substitute their x and y values into the slope formula
`m = (y_2-y_1)/(x_2-x_1)` and solve:

`m = ((5)-(2))/((4)-(0)) \\m = (5-2)/(4-0) \\m = (3)/(4)`

Thus, the slope is
`(3)/(4)`.

2) Next, find the y-intercept of the line by looking at the graph. The y-intercept is the point at which the line intersects the y-axis. By reading the graph, we can see that that point is (0,2), thus 2 is the y-intercept.

3) Now, using the slope-intercept formula
`y = mx + b`, substitute the found values for the
`m` and the
`b` to write the equation of the line.

Since
`m` represents the slope, substitute
`(3)/(4)` in its place. Since
`b` represents the y-intercept, substitute 2 in its place. This gives the following answer and equation:

`y = (3)/(4) x+2`

Answer 2

Y=3\4+2

Slope=rise/run. 3\4
Y-intercept = 2