Question

learning target: i can create a function to model linear relationships from multiple representations. (2 pts)

part a
slope =

part b
y-intercept =

part c
slope intercept equation:

19 part a
(a) a line passes through the points (3, 5) and (2, 0).
what is the slope of the line?
a ( m = 6 )
b ( m = 5 )
c ( m = -5 )
d ( m = -6 )

Explanation:

Part A (First Problem: Slope)

Step1: Identify two points

We have points \((0, -5)\) and \((3, -1)\).

Step2: Use slope formula \(m=\frac{y_2 - y_1}{x_2 - x_1}\)

Substitute \(x_1 = 0,y_1=-5,x_2 = 3,y_2=-1\) into the formula: \(m=\frac{-1-(-5)}{3 - 0}=\frac{-1 + 5}{3}=\frac{4}{3}\)? Wait, no, wait the first problem's points: Wait, the first graph has \((0,-5)\) and \((3,-1)\)? Wait, no, let's re - check. Wait, the first problem's graph: the y - intercept is \((0,-5)\) and another point is \((3,-1)\)? Wait, no, maybe I misread. Wait, the first problem: the line passes through \((0,-5)\) and \((3,-1)\)? Wait, no, let's calculate slope correctly. The slope formula is \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Let \( (x_1,y_1)=(0,-5)\) and \( (x_2,y_2)=(3,-1)\). Then \(m=\frac{-1-(-5)}{3 - 0}=\frac{-1 + 5}{3}=\frac{4}{3}\)? Wait, that can't be. Wait, maybe the points are \((0,-5)\) and \((3,-1)\)? Wait, no, maybe I made a mistake. Wait, the second problem (question 19 part a) is about points \((3,5)\) and \((2,0)\). Let's solve that first.

Question 19 Part A

Step1: Recall slope formula

The slope \(m\) between two points \((x_1,y_1)\) and \((x_2,y_2)\) is given by \(m=\frac{y_2 - y_1}{x_2 - x_1}\).

Step2: Substitute the points

We have \((x_1,y_1)=(3,5)\) and \((x_2,y_2)=(2,0)\). Substitute into the formula: \(m=\frac{0 - 5}{2 - 3}=\frac{-5}{-1}=5\).

Step1: Identify points

The line passes through \((0,-5)\) (y - intercept) and \((3,-1)\).

Step2: Apply slope formula

Using \(m=\frac{y_2 - y_1}{x_2 - x_1}\), with \(x_1 = 0,y_1=-5,x_2 = 3,y_2=-1\), we get \(m=\frac{-1-(-5)}{3-0}=\frac{4}{3}\)? Wait, no, wait the graph: maybe the points are \((0,-5)\) and \((3,-1)\)? Wait, no, let's check the y - intercept. The y - intercept is where \(x = 0\), so \((0,-5)\) is correct. Another point is \((3,-1)\). So slope \(m=\frac{-1-(-5)}{3 - 0}=\frac{4}{3}\)? Wait, that seems odd. Wait, maybe the point is \((3,-1)\) and \((0,-5)\). So the change in y is \(-1-(-5)=4\), change in x is \(3 - 0 = 3\), so slope is \(\frac{4}{3}\).

Part B: y - intercept

Answer:

B. \(m = 5\)

First Problem (Part A, B, C)

Part A: Slope