in the equation of the line: y - 2 = 2/3(x + 1), what point does the line pass through?

Answer 1

y-2 = (2/3)(x+1)

y = 2x/3 + 2/3 +2

y = 2x/3 +8/3 the y intercept = 8/3 = 2 2/3, the point (0, 8/3)

the x coordinate is when y=0 = 2x/3+8/3

2x = -8

x =-4 which is the point (-4,0)

the line goes through both intersects, through the points (0, 8/3) and (-4,0)

and other points in quadrants I, II, and III, but never any points in quadrant IV

Answer 2

The simplest way to figure out this problem is to get the line into y=mx+b (slope-intercept) form.

So first we distribute the ²/₃ by multiplying to get ²/₃x + ²/₃.

Then add 2 to both sides to get y by itself and we end up with our new equation of y=²/₃x + ⁸/₃.

You can graph that line on a coordinate grid or plug in numbers for x to find whichever point you're looking for, for example:

y = ²/₃(3) + ⁸/₃ y = ²/₃(5) + ⁸/₃ y = ²/₃(8) + ⁸/₃

y = 2 + ⁸/₃ y = ¹⁰/₃ + ⁸/₃ y = ¹⁶/₃ + ⁸/₃

y = ¹⁴/₃ y = ¹⁸/₃ = 6 y = ²⁴/₃ = 8

(3, ¹⁴/₃) (5,6) (8,8)