Question

Find a linear equation whose graph is the straight line with the given property.
Through (2, −7) and (1, 1)

I got -8x-23, I know it doesn't match, maybe its the wrong formula

Find a linear equation whose graph is the straight line with the given property.
Through
(1/4, −1)and parallel to the line
4x − 5y = 5

How do I make it parallel?

Thank you.

Answer 1

slope = (1+7)/(1-2) = -8

I don't know what method or "formula" you have been taught, but using the slope-yintercept form seems to be a popular method these days.

y = mx + b
y = -8x + b
sub in the point (1,1) , (I always use the "easier" point)
1 = -8 + b
b = 9

equation : y = -8x + 9
or
8x + y = 9

The second one is even easier.
Since the new line is parallel to the given line, it must look like
4x - 5y = c , differing only in the constant term
sub in the given point (1/4 , -1)
4(1/4) - 5(-1) = c
c = 1 + 5 = 6

new equation: 4x - 5y = 6