Question

find the slope of the equation and the graph. do they have the same slopes?
y = -2x + 3
draw
slope of equation =
slope of graph =
yes, the slopes are the same. no, the slopes are not the same.

Explanation:

Step1: Find slope of equation

The equation is in slope - intercept form \(y = mx + b\), where \(m\) is the slope. For \(y=-2x + 3\), the slope \(m=-2\).

Step2: Find slope of graph

We can use two points on the graph. Let's take the points \((0, - 1)\) and \((1,2)\) (from the graph). The slope formula is \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Substituting \(x_1 = 0,y_1=-1,x_2 = 1,y_2 = 2\), we get \(m=\frac{2-(-1)}{1 - 0}=\frac{3}{1}=3\). Wait, maybe I picked the wrong points. Let's look again. Wait, the equation is \(y=-2x + 3\), but the graph seems to have a different slope. Wait, maybe the points are \((1,2)\) and \((2,5)\)? Wait, no, let's recalculate. Wait, the equation \(y=-2x + 3\) has a slope of \(-2\), but the graph: let's take two points. Let's say when \(x = 0\), the equation gives \(y = 3\), but the graph at \(x = 0\) has \(y=-1\). Wait, maybe there is a mistake in my point selection. Wait, the graph has points: let's see, one point is \((1,2)\), another is \((0,-1)\), and another is \((2,5)\). Wait, the slope between \((0,-1)\) and \((1,2)\) is \(\frac{2-(-1)}{1-0}=3\), between \((1,2)\) and \((2,5)\) is \(\frac{5 - 2}{2-1}=3\). The equation \(y=-2x + 3\) has slope \(-2\), so the slopes are different.

Answer:

Slope of equation \(=-2\)
Slope of graph \(=3\)
No, the slopes are not the same.