Question

1 what is the slope and y-intercept of the following line?
y = 3x + 1
answer:
3 write an equation for the graphed line.

Explanation:

Question 1:

Step1: Recall slope - intercept form

The slope - intercept form of a line is $y = mx + b$, where $m$ is the slope and $b$ is the $y$-intercept.

Step2: Identify $m$ and $b$ in $y = 3x+1$

For the equation $y = 3x + 1$, comparing with $y=mx + b$, we have $m = 3$ (slope) and $b = 1$ ($y$-intercept).

Step1: Calculate the slope ($m$)

The formula for slope between two points $(x_1,y_1)$ and $(x_2,y_2)$ is $m=\frac{y_2 - y_1}{x_2 - x_1}$. Using the points $(0,3)$ and $(3,0)$:
$m=\frac{0 - 3}{3-0}=\frac{- 3}{3}=- 1$

Step2: Find the $y$-intercept ($b$)

The $y$-intercept is the value of $y$ when $x = 0$. From the point $(0,3)$, when $x = 0$, $y=3$, so $b = 3$.

Step3: Write the equation in slope - intercept form

Using $y=mx + b$ with $m=-1$ and $b = 3$, the equation is $y=-x + 3$.

Answer:

Slope is $3$, $y$-intercept is $1$

Question 3:

To write the equation of the graphed line, we first need to find two points on the line. From the graph (assuming the grid is with integer coordinates), let's assume two points. Let's say the line passes through $(0, 3)$ and $(3, 0)$ (we can find these by looking at the intersection of the line with the grid lines).