Question

Question What is the equation of the line in the graph? Enter your answer in the boxes.

Answer 1

Answer: The equation of the line in the graph is:
`y = (3)/(4) x-(7)/(4)`

Explanation:

Question: What is the equation of the line in the graph?

The standard equation of a line is: y = mx + b

Where m = slope and b = y-intercept.

Lets start with the slope:

The slope of a line is a measure of its steepness.

slope = m =
`(rise)/(run)` =
`(y_(2)-y_(1) )/(x_(2)-x_(1) )`

(
`x_(1)`,
`y_{1`) = coordinates of first point in the line

(
`x_(2)`,
`y_(2)`) = coordinates of second point in the line

slope = m =
`(rise)/(run)` =
`(2--1)/(5-1)` =
`(3)/(4)`

(1, -1) = coordinates of first point in the line

(5, 2) = coordinates of second point in the line

Slope =
`(3)/(4)`

Lets find the y-intercept:

The y-intercept is the point where the graph intersects the y-axis.

Since the y-intercept is not visible number on the graph we can solve it by using a coordinate from the graph, and plugging it into the equation of a line with the slope (3/4).

Step 1: form equation of a line (with slope value we found)

y = 3/4x + b

Step 2: plug in coordinate (1, -1)

-1 = 3/4(1) + b

Step 3: Solve for b (y-intercept).

-1 = 3/4 + b

-1 - 3/4 = b

-4/4 - 3/4 = b

b = -7/4

The y-intercept = -7/4

So the equation of the line in the graph is:
`y = (3)/(4) x-(7)/(4)`