algebra 1 homework help

Question

How do I find slope intercept form and point slope form for this algebra problem?

passing through point (-2, 2) and parallel to equation 2x-3y-7=0. please show steps

Answer 1

Slope intercept form line equation is y = mx + b. where m -slope and b is y -intercept.  

Step 1. First find the slope of the line.

The line is parallel to the given line 2x - 3y = 7

Rewrite the equation in slope-intercept form to find the slope m

2x - 3y = 7

Subtract 2x from each side

2x -3y - 2x= 7 -2x

-3y =   -2x + 7

Divide each side by -3

y =   2/3x - 7/3

slope m =2/3

Paralel lines has same slope. So, parallel line equation slope is 2/3   

Step 2. Next find the y - intercept.

y -intercept value (b) value can be found by replacing the x and y coordinate values in the equation with the given point (-2, 2)

 y = 2/3x + b

 2 = 2/3 * -2 + b

 2 = -4/3   + b

Add 4/3 to each side

 2 + 4/3= -4/3   +4/3 + b

 b = (3 * 2 +4)/3 = 10/3

 Step 3. Write the final line equation

 Replace m = 2/3 and b = 10/3 in slope-intercept form line equation y = mx + b

 y = 2/3x + 10/3.