Question

graph the following features: • y-intercept = 1 • slope = $-\frac{5}{3}$

Explanation:

Step1: Plot the y - intercept

The y - intercept is the point where the line crosses the y - axis. Given that the y - intercept is 1, we plot the point (0, 1) on the coordinate plane.

Step2: Use the slope to find another point

The slope of a line is given by the formula $m=\frac{\text{rise}}{\text{run}}$. Here, the slope $m =-\frac{5}{3}$. The negative sign means we will go down (for the rise) and the fraction $\frac{5}{3}$ means we go down 5 units and then 3 units to the right (or up 5 units and 3 units to the left, but since the slope is negative, down and right is more intuitive for graphing).
Starting from the point (0, 1), if we go down 5 units (since the rise is - 5) and then 3 units to the right (run is 3), we get to the point $(0 + 3,1-5)=(3,-4)$.
We can also go up 5 units and 3 units to the left. Starting from (0,1), moving up 5 units gives $y = 1+5 = 6$ and moving 3 units to the left gives $x=0 - 3=-3$, so we get the point $(-3,6)$.

Step3: Draw the line

Now that we have two points, (0, 1) and either (3, - 4) or (-3,6), we can draw a straight line passing through these points.

(Note: Since the problem is about graphing, the final answer is the graph of the line with y - intercept 1 and slope $-\frac{5}{3}$ passing through the points we found. If we were to write the equation of the line, it would be $y=-\frac{5}{3}x + 1$ using the slope - intercept form $y=mx + b$ where $m =-\frac{5}{3}$ and $b = 1$.)

Answer:

The graph is a straight line passing through the points (0, 1) and (3, - 4) (or (-3, 6)) with a slope of $-\frac{5}{3}$ and y - intercept at (0, 1). The equation of the line is $y =-\frac{5}{3}x+1$.