Write an equation in slope-intercept form of the line that passes through (2,2) and has a y-intercept of 7?

Question

So I was supposed to write an equation in slope-intercept form that passes through (2,2) and the y-intercept is 7.

Now I thought this means I turn the points on the line into the slope, so 2/2... and this would make the equation y = 2/2x + 7 but my math book says it's y = -5/2x + 7 and my teacher didn't help at all and I have to know how to solve these to pass my exam so please help!!

Answer 1

Slope intercept equation is y=mx+b. If it says you have a y-intercept of 7, the 7 replaces the b because the b is "y-intercept". So now you have y=mx+7. The point (2,2) refers to x and y. So you plug in 2 and 2 for x and y in the equation. 2=m2+7. To solve for m you have to isolate it, so you subtract seven from each side (-5=m2) and then you divide each side by 2 (-5/2=m). Now you have the information for your equation. . .m=-5/2 and b=7!

y= -5/2x+7

That's how you do the problems with the example above. There's another kind of question they might ask and that is "Write an equation with the given points - (2,-4) and (4,1). Now what you do here is put those numbers in Point Slope form. And that form is (Y sub 2 - Y sub 1) divided by (X sub 2 - X sub 1). If you plug in those numbers the Y sub and X sub 2's are really the SECOND numbers in the coordinates. . .Y sub 2 is 1 and Y sub 1 is -4. X sub 2 is 4 and and X sub 1 is 2. That equation if you solve it right will give you the slope of the equation. The slope of this equation would be 5/2. Then you plug that in to y=mx+b...y=5/2x+b. To find the X and Y values, use the coordinates of the first ordered pair (2,-4) and plug those in. Then solve for b.

Answer 2

OK I'm NOT a high school maths teacher, so it may pay to check with someone else! But at the time of me typing I seem to be all you have (hopefully someone else will come along!), so here goes...

On your graph, put a dot at 2,2 (ie, 2 squares across and 2 squares up). Put another dot at 7 on the y-axis. Join them.

You will see that the line goes down 5 squares for every 2 squares it goes across to the right. Because it goes DOWN 5 squares it is "-5". Because it goes 2 to the RIGHT it is "2". (Left would be "-2").

So you have the "-5/2" part.

The +7 is just where it intercepts the y-axis. And an intercept equation is what you want. So put "y=" on the start and "+7" on the end.

Now you have "y=-5/2+7".

I'm sure there's a better explanation!

Answer 3

Dear friend

first of all the eqn in slope intercept form is y=mx+c
x=y=2,c=7
substituting
2=2m+7
2m= 2-7
m=-5/2
and hence the answer is
y=(-5x/2) + 7

Answer 4

okay,
the equation is y=mx+b
first lets substitute in the y-intercept
so we have, y=mx+7
now lets substitute in the x and the y of the ordered pair,
so we have, 2=m(2)+7
now lets solve this equation for m
first minus 7 on each side,
so we have, -5=m(2)
now lets divide by two on each side,
so we've solved this, -5/2=m
now to make a complete slop intercept equation, you have to always have the m and the b filled in, so if we do that we have:

y=-5/2x+7


Sorry if this is confusing, its kinda hard to explain on the computer