Let's recall the slope-intercept form of a line. y=mx+b Here, m represents the slope and b the y-intercept. Let's identify the slope and the y-intercept of the line in the graph.
Consider the given graph.
We can see that the function intercepts the y-axis at the point (0,2). This means the y-intercept is b=2.
To find the slope, we will trace along the line of the given graph until we find a lattice point, which is a point that lies perfectly on the grid lines. By doing this, we will be able to identify the slope using rise and run of the graph.
Here we have identified (5,-1) as our second point. From the y-intercept to this point, we move 5 steps horizontally in the positive direction. Then, we move 3 steps vertically in the negative direction. m=runrise=5-3⇔m=-53
Now that we have the slope and the y-intercept, we can write our final equation. y=mx+b⇒y=-53x+2 The correct choice is D.