Question

An illustration of a coordinate plane with four quadrants shows the x-axis ranging from negative 9 to 9 and the y-axis ranging from negative 11 to 11 in increments of 1. A solid upward line with arrows at both ends is plotted on the graph. The line passes through the plotted points left parenthesis 0 comma 4 right parenthesis and left parenthesis 1 comma 8 right parenthesis.

Derive the equation of the line in slope-intercept form.








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Answer 1

To find the equation of the line in slope-intercept form, we first need to calculate the slope of the line using the two given points.

The slope formula is:
m = (y2 - y1) / (x2 - x1)

Using the points (0,4) and (1,8):
m = (8 - 4) / (1 - 0)
m = 4 / 1
m = 4

Now that we have the slope, we can use one of the given points and the slope to find the y-intercept.

Using (0,4):
y = mx + b
4 = 4(0) + b
4 = b

So the y-intercept is 4.

Therefore, the equation of the line in slope-intercept form is:
y = 4x + 4