Find the x-intercept and y-intercept

by Julee
(USA)

Question
Find the x- and y- intercepts of the line using these coordinates, (–2, –5) and (6, 1).

Answer
STEP 1:    Before getting started, it will be helpful if you could recollect the basic definition of the intercepts. By the x-intercepts, we mean the x-coordinate of a point where a graph crosses the x-axis. Similarly, y-intercept refers to the y-coordinate of a point where a graph crosses the y-axis.

To find the intercepts, we either need the graph or the equation defining the graph. Since we are given only two coordinate points, you will need to frame the equation using these points and then find the intercepts.

STEP 2:    You can use the slope-intercept form to find the equation of the line. By the slope-intercept form, we refer to an equation of the form:
                                        y = mx + b

Make a note of what each variable in the equation stands for:

slope and y intercept

Since the value of m is unknown, the first step is to calculate the slope of the line.

STEP 3:   If (x1, y1) and (x2, y2) are two coordinate points through which a line passes, then the slope of the line defined by these points is:

slope formula

Choose (x1, y1) = (–2, –5) and (x2, y2) = (6, 1).

using the slope formula

By substituting the value obtained in the slope-intercept form, you get the equation:

the slope, m is calculated as 3/4

STEP 4:    The value of b is still unknown. Since the line is said to pass through (–2, –5) and (6, 1), select either of the points and substitute the respective values for x and y. We shall select the point (6, 1).

finding for the y-intercept b

STEP 5:    Now, solve the equation for b.

calculating for the y-intercept b

With the values obtained for m and b, the equation of the line takes the form:
the equation of the line

STEP 6:    Now, you can easily find the intercepts. By referring to the definition, we understand that the y-intercept is some coordinate point like (0, y), and the
x-intercept is (x, 0).

Since the x-coordinate is 0 for y-intercept, substitute the 0 for x in the equation.

calculating for the y-intercept
Similarly, find the x-intercept by replacing y with 0.
calculating for the x-intercept

You finally get the x-intercept as (14/3,0),and the y-intercept as (0,-7/2).

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