Answer (assuming it can be in slope-intercept form):
[tex]y = \frac{3}{4} x+2[/tex]
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 [tex]m = \frac{y_2-y_1}{x_2-x_1}[/tex] and solve:
[tex]m = \frac{(5)-(2)}{(4)-(0)} \\m = \frac{5-2}{4-0} \\m = \frac{3}{4}[/tex]
Thus, the slope is [tex]\frac{3}{4}[/tex].
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 [tex]y = mx + b[/tex], substitute the found values for the [tex]m[/tex] and the [tex]b[/tex] to write the equation of the line.
Since [tex]m[/tex] represents the slope, substitute [tex]\frac{3}{4}[/tex] in its place. Since [tex]b[/tex] represents the y-intercept, substitute 2 in its place. This gives the following answer and equation:
[tex]y = \frac{3}{4} x+2[/tex]
