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? (4 points)
y = 3 over 4.x + 4
y = 4 over 3.x + 4
y = 4x + 3 over 4.
y = 4x + 4 over 3.
To determine the equation of the line, we first need to find the slope of the line. We can do this by using the two given points (-4, 1) and (0, 4) that lie on the line.
The formula for finding the slope of a line passing through two points (x1, y1) and (x2, y2) is given by:
slope = (y2 - y1) / (x2 - x1)
Using (-4, 1) and (0, 4), the slope is:
slope = (4 - 1) / (0 - (-4))
slope = 3 / 4
Now that we have the slope, we can use the point-slope equation of a line to find the equation. The point-slope equation is:
y - y1 = m(x - x1)
Using the point (-4, 1) and the slope 3/4, we substitute the values into the equation:
y - 1 = (3/4)(x - (-4))
y - 1 = (3/4)(x + 4)
y - 1 = (3/4)x + 3
y = (3/4)x + 3 + 1
y = (3/4)x + 4
Therefore, the equation that represents the line passing through the point (-4, 1) and through the y-axis at 4 is:
y = (3/4)x + 4
Thus, the correct answer is: y = 3 over 4.x + 4.