Question

name
9.6 hw
write the equation of the line with the give

1. slope is -3 and a y-intercept of 7

write an equation based on the graph.
3.

Explanation:

Problem 1: Write the equation of the line with slope -3 and y - intercept 7

Step 1: Recall the slope - intercept form

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

Step 2: Substitute the given values

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

Step 1: Calculate the slope

The formula for the slope \(m\) between two points \((x_1,y_1)\) and \((x_2,y_2)\) is \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Let \((x_1,y_1)=(0,-1)\) and \((x_2,y_2)=(4,1)\). Then \(m=\frac{1-(-1)}{4 - 0}=\frac{1 + 1}{4}=\frac{2}{4}=\frac{1}{2}\).

Step 2: Determine the y - intercept

The y - intercept \(b\) is the value of \(y\) when \(x = 0\). From the point \((0,-1)\), when \(x = 0\), \(y=-1\), so \(b=-1\).

Step 3: Write the equation in slope - intercept form

Using the slope - intercept form \(y=mx + b\) with \(m=\frac{1}{2}\) and \(b=-1\), we get \(y=\frac{1}{2}x-1\).

(Note: If the actual points on the graph are different, recalculate the slope and y - intercept accordingly. For example, if the line passes through \((0, - 2)\) and \((5,0)\), the slope \(m=\frac{0-(-2)}{5-0}=\frac{2}{5}\) and \(b=-2\), so the equation is \(y=\frac{2}{5}x-2\))

Answer:

\(y = - 3x+7\)

Problem 3: Write an equation based on the graph (assuming we can identify two points on the line. Let's assume from the graph we can find two points, for example, let's say the line passes through \((0,-1)\) and \((4,1)\) (we need to estimate from the grid, let's assume these points for demonstration. If the actual points are different, the method is similar))