Question

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

Answer 1

Y=3\4+2

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

Answer 2

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

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

Step-by-step 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 $m = \frac{y_2-y_1}{x_2-x_1}$ and solve:

$m = \frac{(5)-(2)}{(4)-(0)} \\m = \frac{5-2}{4-0} \\m = \frac{3}{4}$

Thus, the slope is $\frac{3}{4}$.

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 $\frac{3}{4}$ in its place. Since $b$ represents the y-intercept, substitute 2 in its place. This gives the following answer and equation:

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