Question

lesson practice
determine the slope and the y-intercept of the equation.
(ex 1)
a. $y = 0.7x - 4.9$ b. $-9x + 3y = 12$
graph each line using the equation that is in slope-intercept form.
(ex 2)
c. $y = \frac{3}{5}x$ d. $x - 4y - 20 = 0$
write the equation of the graphed line in slope-intercept form.
(ex 3)
e. write the equation of the graphed line in slope-intercept form.

Explanation:

Part a: Determine slope and y - intercept of \(y = 0.7x-4.9\)

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: Identify \(m\) and \(b\) from the given equation

For the equation \(y = 0.7x-4.9\), comparing it with \(y=mx + b\), we have \(m = 0.7\) (slope) and \(b=- 4.9\) ( \(y\) - intercept).

Step1: Convert to slope - intercept form

We need to solve the equation \(-9x + 3y = 12\) for \(y\).
Add \(9x\) to both sides: \(3y=9x + 12\).
Divide each term by 3: \(y=\frac{9x}{3}+\frac{12}{3}\), which simplifies to \(y = 3x+4\).

Step2: Identify \(m\) and \(b\)

Comparing \(y = 3x + 4\) with \(y=mx + b\), we get \(m = 3\) (slope) and \(b = 4\) ( \(y\) - intercept).

Step1: Recall slope - intercept form properties

The equation \(y=\frac{3}{5}x\) is in slope - intercept form \(y = mx + b\) with \(m=\frac{3}{5}\) and \(b = 0\). So the line passes through the origin \((0,0)\) (since \(b = 0\)).

Step2: Use the slope to find another point

The slope \(m=\frac{\text{rise}}{\text{run}}=\frac{3}{5}\). From the origin \((0,0)\), move up 3 units (rise) and then 5 units to the right (run) to get the point \((5,3)\).

Step3: Draw the line

Draw a line through the points \((0,0)\) and \((5,3)\).

Answer:

Slope \(m = 0.7\), \(y\) - intercept \(b=-4.9\)

Part b: Determine slope and y - intercept of \(-9x + 3y=12\)