Question

graph the following features: • y-intercept = -5 • slope = 2

Explanation:

Step1: Recall the slope - intercept form

The slope - intercept form of a linear equation is $y = mx + b$, where $m$ is the slope and $b$ is the y - intercept. Given that the slope $m = 2$ and the y - intercept $b=-5$, the equation of the line is $y=2x - 5$.

Step2: Plot the y - intercept

The y - intercept is the point where $x = 0$. So, when $x = 0$, $y=-5$. We plot the point $(0,-5)$ on the coordinate plane.

Step3: Use the slope to find another point

The slope $m = 2=\frac{\text{rise}}{\text{run}}=\frac{2}{1}$. Starting from the point $(0,-5)$, we move up 2 units (because the rise is 2) and then 1 unit to the right (because the run is 1). This gives us the point $(0 + 1,-5+2)=(1,-3)$. We can also move down 2 units and 1 unit to the left from $(0,-5)$ to get another point $(- 1,-7)$ (since $0-1=-1$ and $-5 - 2=-7$).

Step4: Draw the line

After plotting the points (e.g., $(0,-5)$ and $(1,-3)$), we draw a straight line passing through these points.

(Note: Since the question is about graphing, the final answer is the graph of the line $y = 2x-5$ with the y - intercept at $(0,-5)$ and a slope of 2. To represent the graph, we have the line passing through points like $(0,-5)$, $(1,-3)$, $(-1,-7)$ etc. on the given coordinate grid.)

Answer:

The graph is a straight line with a y - intercept at the point \((0, - 5)\) and a slope of 2, following the equation \(y=2x - 5\). The line passes through points such as \((0,-5)\), \((1,-3)\), \((-1,-7)\) (and other points obtained by using the slope) on the provided coordinate plane.