Question

find the slope of the equation and the graph. do they have the same slopes?
y = -3x + 6
show your work here
slope of equation =
slope of graph =

Explanation:

Step1: Find slope of equation

The equation is in slope - intercept form \(y = mx + b\), where \(m\) is the slope. For \(y=-3x + 6\), the slope \(m=-3\).

Step2: Find slope of graph

We can use two points on the graph. From the graph, we can see the points \((0,2)\), \((1,4)\) and \((2,6)\) (we can choose any two). Using the slope formula \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Let's take \((0,2)\) and \((1,4)\). Then \(m=\frac{4 - 2}{1 - 0}=\frac{2}{1}=2\). Wait, but the equation has slope - 3. Wait, maybe I misread the graph. Wait, the equation is \(y =- 3x+6\), but the graph's points: let's check again. Wait, the y - intercept of the equation is 6, but the graph has a y - intercept of 2? Wait, maybe there is a mistake in my initial point selection. Wait, no, the user's graph: the blue line has a y - intercept at (0,2), then (1,4), (2,6). So the slope of the graph is \(\frac{4 - 2}{1 - 0}=2\), and the slope of the equation is - 3. So they are not the same. But let's do it properly.

Wait, the equation is \(y=-3x + 6\), so slope of equation is - 3. For the graph, let's take two points. Let's say \((x_1,y_1)=(0,2)\) and \((x_2,y_2)=(1,4)\). Then slope \(m=\frac{y_2 - y_1}{x_2 - x_1}=\frac{4 - 2}{1 - 0}=2\). So slope of equation is - 3, slope of graph is 2. So they are not the same. But maybe I made a mistake in the graph's points. Wait, the original equation is \(y=-3x + 6\), so when \(x = 0\), \(y = 6\); when \(x = 1\), \(y=-3(1)+6 = 3\); when \(x = 2\), \(y=-3(2)+6 = 0\). But the graph has points (0,2), (1,4), (2,6), which is a line with slope 2, equation \(y = 2x+2\). So the slope of the equation \(y=-3x + 6\) is - 3, slope of the graph is 2. So they are not the same.

Answer:

Slope of equation: \(-3\)
Slope of graph: \(2\)
They do not have the same slopes.