Find the x-intercept and y-intercept

by Julee

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

Comments for Find the x-intercept and y-intercept

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Feb 26, 2021
yay NEW
by: Blue Orangeade

The layout of this lesson was kind of hard to read, but overall I guess it was good. Homework help hehe

Jan 15, 2021
Awesome NEW
by: Anonymous

This thing right here really has helped me do my homewok Thats why its getting five stars

Dec 11, 2020
Dumb NEW
by: Anonymous

This really just asked me to pay 99 to learn the lesson, what a scam.

Nov 14, 2019
by: Anonymous

Find the y-intercept of the following:

x: 1, 2, 3, 4, 5
y: 2, 4, 5, 5, 7

Nov 05, 2019
Good formula math done wrong
by: Anonymous

you should have got a negative y-intercept AND a NEGATIVE x-intercept.

May 10, 2019
by: Anonymous

Yeah so it was wrong, thanks for your help =)

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