Question

9.6 notes – writing linear equations in slope-intercept form
identify the initial value (y-intercept) from a table, graph, equation, or verbal description.
use the slope and y-intercepts to write a linear function in the form ( y = mx + b ) from any representation (table, graph, or verbal description).
graph a linear equation given an equation.
slope-intercept form ( y = mx + b )
( m ) is the
( b ) is the
write the equation of a line given the slope and y-intercept.
write the equation of the line with the given slope and y-intercept.

1. slope is ( -2 ) and a y-intercept of 5
2. slope is ( \frac{3}{4} ) and y-intercept is ( -3 )

write the equation of a line in slope intercept form given a graph.
3)
slope:
y-intercept:
equation:
4)
slope:
y-intercept:
equation:

Explanation:

Problem 1:

Step1: Recall 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.

Step2: Substitute \(m=-2\) and \(b = 5\)

Substitute \(m=-2\) (slope) and \(b = 5\) (y - intercept) into the equation \(y=mx + b\).
We get \(y=-2x + 5\).

Step1: Recall 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.

Step2: Substitute \(m = \frac{3}{4}\) and \(b=-3\)

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

Step1: Find the slope

The formula for slope \(m=\frac{y_2 - y_1}{x_2 - x_1}\). We have two points \((0,-5)\) (where \(x_1 = 0,y_1=-5\)) and \((3,-1)\) (where \(x_2 = 3,y_2=-1\)).
\(m=\frac{-1-(-5)}{3 - 0}=\frac{-1 + 5}{3}=\frac{4}{3}\)

Step2: Find the y - intercept

The y - intercept \(b\) is the value of \(y\) when \(x = 0\). From the point \((0,-5)\), when \(x = 0\), \(y=-5\), so \(b=-5\).

Step3: Write the equation

Using the slope - intercept form \(y=mx + b\) with \(m=\frac{4}{3}\) and \(b=-5\), we get \(y=\frac{4}{3}x-5\).

Answer:

\(y=-2x + 5\)

Problem 2: