Question

A straight line in the coordinate plane passes through the points with (x,y) coordinates (–1,1) and (2,3). What are the (x,y) coordinates of the point at which the line passes through the y-axis?
A) (-2, 0)
B) ( 0, 2/3)
C) ( 0, 5/3)
D) (0,2)
E) (0, 5/2)

Answer 1

first find the slope of the line passing through (-1,1) and (2,3) by using the slope formula, or the easier way, by graphing the two points and counting up 2 from the first point then over 3 to the second point, which means your slope is 2/3, or m = 2/3. Substitute that into the slope-intercept formula: y = mx + b, or y = 2/3 x + b. now, take either one of the two points given, (-1, 1) or (2,3), and substitute the x and y values into the equation
y = 2/3 x + b, and solve the equation for b.
if you use the point (2, 3), then you would substitute it in like this:
3 = (2/3) 2 + b
3 = 4/3 + b
3 - 4/3 = b
9/3 - 4/3 = b
5/3 = b
The y-intercept is 5/3