# Math Help - Inverse Problems Functions

1. ## Inverse Problems Functions

Explain best you can and if possible please just give answers i have to go to sleep dont know if i can finish in morning

2. A linear equation has the form y=mx+c.

In the first set you are given m. Substitute the points and then rearrange to find c. So for the first question,
y = -2x+c and (x,y) = (2,1)
1 = -2(2)+c
1=-4+c
1+4 =c
c=5.
y = -2x+5

In the second set you are given 2 points. Call them $(x_1,y_1)$ and $(x_2, y_2)$, and use the formula $m = \frac{y_2-y_1}{x_2-x_1}$, then use the method for the first set.
The first question looks like this:
$(x_1,y_1) = (2,3)$ and $(x_2,y_2) = (5,9)$
$m = \frac{9-3}{5-2}$
$=\frac{6}{3}$
=2

y = 2x+c
3=2(2)+c
3=4+c
3-4 = c
c=-1
y=2x-1

3. Originally Posted by HamzaH

Explain best you can and if possible please just give answers i have to go to sleep dont know if i can finish in morning
This is not a site for doing your homework.

Option 1: Use the model $y - y_1 = m (x - x_1)$.

For m = 3 and (-1, -10): $y - (-10) = 3 (x - (-1)) \Rightarrow y = 3x - 7$.

Option 2: Use the model $y = mx + c$.

For m = 3 and (-1, -10): $y = 3x + c$. Substitute (-1, -10) and solve for c: -10 = -3 + c => c = -7.

Note that f(5) = -1 etc. means that the point (5, -1) lies on the line.