Could someone help me with a math problem?

Question

f(-3) = 7 and has y-intercept of 5, what is the equation of the line?

Answer 1

*The problem gives you f(-3) = 7 which is f(x) = y before you have values/numbers in the funtion. You have a point (-3,7). The problem gives you the slope (5) represented as "b."

First: place the point & the y-intercept in the slope-intercept formula to find the slope (represented as "m") > y = mx + b

7 = m(-3) + 5
7 = -3m + 5

*Subtract 5 from both sides....

7 - 5 = -3m + 5 - 5
2 = -3m

*Isolate "m" on one side > divide both terms by "-3".....

2/-3 = (-3m)/(-3)
-2/3 = m
m = -2/3

Sec: place the slope (-2/3) & the point (-3,7) in the point-slope formula > y - first y = m(x - first x)

y - 7 = (-2/3)[x - (-3)]
y - 7 = (-2/3)[x + 3]
y - 7 = (-2/3)(x) + (-2/3)(3)
y - 7 = (-2x/3) - 6/3
y - 7 = (-2x/3) - 2

Third: isolate "y" on one side > add "7" to both sides....

y - 7 + 7 = (-2x/3) - 2 + 7
y = (-2x/3) + 5

Answer 2

f(-3)=7 is just another way of saying the line has a point at (-3,7).

The y-intercept is showing you at what point the line crosses the vertical axis. Hence, the line also has a point at (0,5).

The slope can be determined by "rise over run", the differences in y's over differences in x's. This would be (7-5)/(-3-0) = 2/-3 = -(2/3).

The equation of the line is therefore y = (-2/3) x + 5

Answer 3

Basically, they're giving you 2 points which lie on the line: (-3, 7) and (0, 5). Find the slope: m= (5-7)/(0+3) = -2/3

Using y = mx + b, the eqn. is y = (-2/3)x + 5

Answer 4

If f(-3) = 7, then the point (-3, 7) is on the line. But so is the point (0,5). So the slope is (5-7)/(0- -3) = -2/3

So by y = mx + b, f(x) = -2/3 x + 5