Question

open desmos in another window so you can use it to plot points and write the equation of lines.
desmos
1 multiple choice 10 points
what is the equation of the line that goes through the points (-1, 1) and (1, 5)? hint: plot these points in desmos.
○ $y = -2x + 3$
○ $y = 2x + 3$
○ $y = \frac{1}{2}x + 3$
○ $y = 2x + 5$

Explanation:

Step1: Calculate the slope

The slope \( m \) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by \( m=\frac{y_2 - y_1}{x_2 - x_1} \). For points \((-1, 1)\) and \((1, 5)\), we have \( x_1=-1, y_1 = 1, x_2=1, y_2 = 5 \). So \( m=\frac{5 - 1}{1-(-1)}=\frac{4}{2}=2 \).

Step2: Use point - slope form to find the equation

The point - slope form of a line is \( y - y_1=m(x - x_1) \). We can use the point \((-1,1)\) and \( m = 2 \). Substituting these values, we get \( y - 1=2(x+1) \).
Expanding the right - hand side: \( y - 1=2x + 2 \).
Adding 1 to both sides: \( y=2x+3 \). We can also check by substituting the points into the equation. For \( x=-1 \), \( y=2\times(-1)+3=-2 + 3 = 1 \) (which matches the point \((-1,1)\)). For \( x = 1 \), \( y=2\times1+3=2 + 3 = 5 \) (which matches the point \((1,5)\)).

Answer:

B. \( y = 2x + 3 \)