Question

Question

Use the image to answer the 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 negative 2 right parenthesis and left parenthesis 1 comma 3 right parenthesis.

Use the graph to derive the equation of the line in slope-intercept form.

(1 point)

Answer 1

[AI-generated answer — Bot GPT 3.5]

To find the equation of the line in slope-intercept form, we first need to determine the slope of the line. The slope can be found using the formula:

m = (y2 - y1) / (x2 - x1)

where (x1, y1) = (0, -2) and (x2, y2) = (1, 3). Plug in these coordinates:

m = (3 - (-2)) / (1 - 0) = 5 / 1 = 5

Now that we have the slope, we can use the point-slope form of the equation of a line:

y - y1 = m(x - x1)

Using the point (0, -2):

y + 2 = 5(x - 0)

Simplify:

y + 2 = 5x

Subtract 2 from both sides:

y = 5x - 2

Therefore, the equation of the line in slope-intercept form is y = 5x - 2.