Question

Look at the graph shown:

A coordinate plane is shown. A line passes through the point -4 comma 1 and through the y-axis at 4.

Which equation best represents the line?

Answer 1

The equation of a line passing through the point (-4,1) and the y-axis at 4 can be determined by finding the slope of the line.

The slope of the line passing through (-4,1) and (0,4) can be calculated as (4-1)/(0-(-4)) = 3/4.

Using the point-slope form of a linear equation, the equation of the line is:

y - 1 = (3/4)(x - (-4))

Simplifying, we get:

y - 1 = (3/4)(x + 4)
y - 1 = (3/4)x + 3
y = (3/4)x + 4

Therefore, the equation representing the line passing through the point (-4,1) and through the y-axis at 4 is y = (3/4)x + 4.