1.Find an equation of the line that passes through (4,3) and is parallel to the line 3x-y=7.

2. Find the equation of the line through (4,3) perpendicular to the line 3x+y=7.
Please show work so I know how to do it

recall the point-slope form for a line.

#1 the slope is 3, so

y-3 = 3(x-4)

Similarly for #2, except the slope is 1/3. (why?)

To find the equation of a line that passes through a given point and is parallel or perpendicular to another line, we can use the following steps:

1. Determine the slope of the given line.
2. Since parallel lines have the same slope, use the slope of the given line to find the slope of the parallel line.
3. Use the slope-intercept form of a line, y = mx + b, where m is the slope and b is the y-intercept.
4. Plug in the coordinates of the given point into the equation and solve for b.

Let's apply these steps to the given questions:

1. Find an equation of the line that passes through (4,3) and is parallel to the line 3x - y = 7.

Step 1: Determine the slope of the given line.
Rewrite the equation in slope-intercept form: y = 3x - 7.
The slope of the given line is 3.

Step 2: Determine the slope of the parallel line.
Since parallel lines have the same slope, the parallel line will also have a slope of 3.

Step 3: Use the slope-intercept form of a line, y = mx + b.
Replace m with 3 to get the equation: y = 3x + b.

Step 4: Plug in the coordinates of the given point into the equation and solve for b.
Using the point (4,3), we have: 3 = 3(4) + b.
Simplifying the equation gives: 3 = 12 + b.
Subtracting 12 from both sides: -9 = b.

Therefore, the equation of the line parallel to the given line and passing through the point (4,3) is: y = 3x - 9.

2. Find the equation of the line through (4,3) perpendicular to the line 3x + y = 7.

Step 1: Determine the slope of the given line.
Rewrite the equation in slope-intercept form: y = -3x + 7.
The slope of the given line is -3.

Step 2: Determine the slope of the perpendicular line.
Since perpendicular lines have slopes that are negative reciprocals, the perpendicular line will have a slope of 1/3.

Step 3: Use the slope-intercept form of a line, y = mx + b.
Replacing m with 1/3, the equation becomes: y = (1/3) x + b.

Step 4: Plug in the coordinates of the given point into the equation and solve for b.
Using the point (4,3), we have: 3 = (1/3)(4) + b.
Simplifying the equation gives: 3 = 4/3 + b.
Subtract 4/3 from both sides: 3 - 4/3 = b.
When calculating, you get: b = 5/3.

Hence, the equation of the line perpendicular to the given line and passing through the point (4,3) is: y = (1/3) x + 5/3.