Can you help me out i need a good grade

Question

Janelle graphed a line through (−6, 5) that had a slope of  -7/9.  What is the y-coordinate of a point on the line that has an x-coordinate of 3?

A) -3

B) -2

C) 2

D) 3

Answer 1

This question can be solved in two parts:

Use the formula, y = mx +b. Plug in the coordinates (-6, 5) and slope (m) of -7/9. Solve for b.

y = mx + b

5 = (-7/9)*(-6) + b

5= (42/9) + b

--- 42/9 reduces to 14/3

5 = 14/3 + b

--- 5 also equals 15/3

15/3 - 14/3 = b

b = 1/3

Since this is the same line, using the value of b from part 1, the slope of (-7/9), and the x-value of 3 (represents a different point on the same line), to solve for y-coordinate:

y= mx + b

y = (-7/9)*(3) + 1/3

y = -21/9 + 1/3

y = -21/9 + 3/9

y = -18/9

y = -2

Answer 2

If it's a multiple choice question, you can approximate without doing all the formal maths for the equation of the line.

Imagine (or draw) the point (-6,5), it is in left/up quadrant (-x, +y)...

slope (or gradient) is -7/9 which means it goes down and to the right (negative gradient)... and gradient is defined as change in y / change in x...

so it will go down 7 units for 9 units to the right.

-6 (x coordinate of point) + 9 (gradient change in x) will bring us to 3 ("a point on the line that has an x-coordinate of 3")...

while 5 (y coordinate of point) - 7 (gradient change in y) will bring us to -2

so point is (3,-2) and answer is B.

Answer 3

The slope of a straight line is given by (y - 5)/(x - (-6)). This slope is set equal to the given slope of -7/9 giving (y - 5)/(x - (-6)) = -7/9. Multiply both sides of the equation by (x - (-6)) to get

y-5 =-7/9 • ((x - (-6)). Add 5 to each side of the equation to get y = -7/9 • (x + 6) +5. This simplifies to y = (-7/9)x - 42/9 + 45/9 which further simplifies to y = -7/9x + 1/3. Substitute x = 3 into the last equation and solve for y.

Answer y = -2