Question

ven slope and y-intercept.

1. slope is \\(\frac{3}{4}\\) and y-intercept is \\(-3\\)

slope intercept form given a graph.
4)
slope:
y-intercept:
equation:

Explanation:

Problem 2 (Given slope and y - intercept)

Step 1: Recall the slope - intercept form

The slope - intercept form of a linear equation is $y = mx + b$, where $m$ is the slope and $b$ is the y - intercept.
We are given that the slope $m=\frac{3}{4}$ and the y - intercept $b = - 3$.

Step 2: Substitute the values into the formula

Substitute $m=\frac{3}{4}$ and $b=-3$ into the equation $y=mx + b$.
We get $y=\frac{3}{4}x-3$.

Step 1: Calculate the slope

The formula for the slope $m$ between two points $(x_1,y_1)$ and $(x_2,y_2)$ is $m=\frac{y_2 - y_1}{x_2 - x_1}$.
We have the points $(0,1)$ (where $x_1 = 0,y_1 = 1$) and $(4,-1)$ (where $x_2=4,y_2=-1$).
Substitute these values into the slope formula: $m=\frac{-1 - 1}{4-0}=\frac{-2}{4}=-\frac{1}{2}$.

Step 2: Determine the y - intercept

The y - intercept $b$ is the y - coordinate of the point where the line crosses the y - axis. From the point $(0,1)$, we can see that when $x = 0$, $y = 1$. So, $b = 1$.

Step 3: Write the equation in slope - intercept form

The slope - intercept form is $y=mx + b$. Substitute $m =-\frac{1}{2}$ and $b = 1$ into the formula.
We get $y=-\frac{1}{2}x + 1$.

Answer:

The equation of the line is $y=\frac{3}{4}x - 3$

Problem 4 (Given a graph)