Answer:
[tex]y = x - 6[/tex]
Step-by-step explanation:
y = mx + b (slope intercept form)
To find the slope you do:
[tex] \frac{y2 - y1}{x2 - x1} [/tex]
[tex]10 = x1 \\ 4 = y1 \\ 3 = x2 \\ - 3 = y2[/tex]
So we put it into the formula:
[tex] \frac{ - 3 - 4}{3 - 10} = \frac{ - 7}{ - 7} = 1[/tex]
Our answer is 1, so that is what slope equals: m = 1
Now we can plug in what we have according to the points we were given and slope we figured out. Let's choose the pair of points: (10,4)
[tex]y = mx + b \\ y = 1x + b[/tex]
For y, we will put 4. For x, we will put 10.
[tex]4 = 1(10) + b[/tex]
Now you just solve for b
1 x 10 is just 10 so now it is:
[tex]4 = 10 + b[/tex]
Now subtract 10 from both sides.
4 - 10 equals -6. 10 - 10 cancels itself out so we get this:
[tex] b = - 6[/tex]
That's the y-intercept answer.
Final answer is:
[tex]y = x - 6 \: \\ or \\ y = 1x - 6[/tex]
