The slope intercept form is
y = mx + c
where m represents the slope (how much y increases, when x grows by 1), and
c is the intercept (the value of y when x=0)
If you have the slope of a line, then any parallel lines will have the same slope.
Any perpendicular line will have a slope of -1/m
Once you have the slope, you then find the intercept by fitting the point on the line.
Example, using number 1.
"parallel to the line y = 4x + 7"
this means that the slope of the new line will also be 4
y = 4x + c
Next, to find the intercept (c), we fit the point given: (x, y) = (-2, 3)
Points are always given in the form (x, y)
So, use the values for the variables:
y = 4x + c
3 = 4(-2) + c
3 = -8 + c
this forces us to use c = 11
the final answer:
y = 4x + 11
This line is parallel to the line y = 4x + 7 (it has the same slope) and it contains the point (-2, 3) because when you put these values for x and y, the equation is true.
3 = 4(-2) + 11
3 = -8 + 11
3 = 3
Yep, it is true.
For the last one (the perpendicular line), don't forget to change the slope to -1/m
The line given is y = 2x + 6
It has a slope of 2
A perpendicular line would have a slope of -1/2
y = (-1/2)x + c
we need to fit the point (x, y) = (-4, 15)
15 = (-1/2)(-4) + c
15 = 2 + c
13 = c
y = (-1/2)x + 13