Question

cycle 1 - homework package
review 3: the equation of a line in slope y - intercept form

1. explain the meaning of m and b in the ( y = mx + b ) equation of a line.
2. for each of the following lines, state the slope and y - intercept and sketch a graph of the line.

a) ( y = 2x + 1 ) b) ( y=-2x + 6 ) c) ( y = x - 3 )

1. for each of the following lines, state the slope and y - intercept and determine the equation of a line in the ( y = mx + b ) form.

(images of graphs for parts a) to f))

1. does the point ( (-5,-20) ) lie on the line ( y = 6x + 10 )? explain
2. does the point ( (6,-10) ) lie on the line ( y =-\frac{5}{3}x - 4 )? explain
3. the point ( (2,a) ) is on the line ( y = 5x - 30 ). determine the value of a.
4. identify whether each of the following linear equations is in standard form. if not, fix it.

a) ( 2x - 3y - 6 = 0 ) b) ( 5x - 2y=-3 ) c) ( y = 2x + 12 ) d) ( 5y + 2x + 25 = 0 ) e) ( \frac{1}{3}x + y - 5 = 0 ) f) ( x + 2y - 10 = 0 ) g) ( -4x - 9y + 4 = 0 )

1. express each of the following equations in slope y - intercept form.

a) ( 7x + y - 4 = 0 ) b) ( 3x + 2y - 8 = 0 ) c) ( x - 4y - 2 = 0 )

1. graph each of the following:

a) ( x - 2y + 6 = 0 ) b) ( 3x + 2y - 1 = 0 ) c) ( x - y = 0 )

Explanation:

Let's solve question 6: "The point (2, a) is on the line \( y = 5x - 30 \). Determine the value of a."

Step 1: Substitute x = 2 into the equation

Since the point (2, a) lies on the line \( y = 5x - 30 \), we substitute \( x = 2 \) into the equation.
\( y = 5(2) - 30 \)

Step 2: Calculate the value of y (which is a)

First, calculate \( 5(2) = 10 \). Then subtract 30: \( 10 - 30 = -20 \). So \( a = -20 \).

Answer:

The value of \( a \) is \(-20\).