Question

name
9.6 hw
write the equation of the line with the g
. slope is -3 and a y-intercept of 7

write an equation based on the graph
.

Explanation:

First Sub - Question: Write the equation of the line with slope - 3 and y - intercept 7

Step1: Recall slope - intercept form

The slope - intercept form of a line is given by \(y=mx + b\), where \(m\) is the slope and \(b\) is the y - intercept.

Step2: Substitute values

We know that \(m=-3\) and \(b = 7\). Substituting these values into the slope - intercept form, we get \(y=-3x + 7\).

Step1: Calculate the slope

The slope \(m\) between two points \((x_1,y_1)\) and \((x_2,y_2)\) is given by \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Let's take the points \((0,0)\) and \((6,2)\). Then \(m=\frac{2-0}{6 - 0}=\frac{2}{6}=\frac{1}{3}\).

Step2: Use slope - intercept form

Since the line passes through the origin \((0,0)\), the y - intercept \(b = 0\). Using the slope - intercept form \(y=mx + b\), with \(m=\frac{1}{3}\) and \(b = 0\), we get \(y=\frac{1}{3}x\).
(Note: If the points on the graph are different, the calculation will change. But based on the visible part of the graph, this is a reasonable assumption.)

Answer:

\(y=-3x + 7\)

Second Sub - Question: Write an equation based on the graph

(Assuming the line passes through the origin \((0,0)\) and the point \((6,2)\) from the grid - like structure, we can calculate the slope first)