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Find the intercepts, then graph

y = - 10x


tell me the 2 plot points please

1 Answer

5 votes

Answer:

The xxx-intercept is the point where a line crosses the xxx-axis, and the yyy-intercept is the point where a line crosses the yyy-axis.

Explanation:

Looking at the graph, we can find the intercepts.

The line crosses the axes at two points:

The point on the xxx-axis is (5,0)(5,0)left parenthesis, 5, comma, 0, right parenthesis. We call this the xxx-intercept.

The point on the yyy-axis is (0,4)(0,4)left parenthesis, 0, comma, 4, right parenthesis. We call this the yyy-intercept.

Want to learn more about finding intercepts from graphs? Check out this video.

Example: Intercepts from a table

We're given a table of values and told that the relationship between xxx and yyy is linear.

xxx yyy

111 -9−9minus, 9

333 -6−6minus, 6

555 -3−3minus, 3

Then we're asked to find the intercepts of the corresponding graph.

The key is realizing that the xxx-intercept is the point where y=0y=0y, equals, 0, and the yyy-intercept is where x=0x=0x, equals, 0.

The point (7,0)(7,0)left parenthesis, 7, comma, 0, right parenthesis is our xxx-intercept because when y=0y=0y, equals, 0, we're on the xxx-axis.

To find the yyy-intercept, we need to "zoom in" on the table to find where x=0x=0x, equals, 0.

The point (0,-10.5)(0,−10.5)left parenthesis, 0, comma, minus, 10, point, 5, right parenthesis is our yyy-intercept.

Want to learn more about finding intercepts from tables? Check out this video.

Example: Intercepts from an equation

We're asked to determine the intercepts of the graph described by the following linear equation:

3x+2y=53x+2y=53, x, plus, 2, y, equals, 5

To find the yyy-intercept, let's substitute \blue x=\blue 0x=0start color #6495ed, x, end color #6495ed, equals, start color #6495ed, 0, end color #6495ed into the equation and solve for yyy:

\begin{aligned}3\cdot\blue{0}+2y&=5\\ 2y&=5\\ y&=\dfrac{5}{2}\end{aligned}

3⋅0+2y

2y

y

=5

=5

=

2

5

So the yyy-intercept is \left(0,\dfrac{5}{2}\right)(0,

2

5

)left parenthesis, 0, comma, start fraction, 5, divided by, 2, end fraction, right parenthesis.

To find the xxx-intercept, let's substitute \pink y=\pink 0y=0start color #ff00af, y, end color #ff00af, equals, start color #ff00af, 0, end color #ff00af into the equation and solve for xxx:

\begin{aligned}3x+2\cdot\pink{0}&=5\\ 3x&=5\\ x&=\dfrac{5}{3}\end{aligned}

3x+2⋅0

3x

x

=5

=5

=

3

5

So the xxx-intercept is \left(\dfrac{5}{3},0\right)(

3

5

,0)left parenthesis, start fraction, 5, divided by, 3, end fraction, comma, 0, right parenthesis.

Want to learn more about finding intercepts from equations? Check out this video.

Practice

PROBLEM 1

Determine the intercepts of the line graphed below.

xxx-intercept:

\Big((left parenthesis

,,comma

\Big))right parenthesis

yyy-intercept:

\Big((left parenthesis

,,comma

\Big))right parenthesis

Find the intercepts, then graph y = - 10x tell me the 2 plot points please-example-1
User Coen Damen
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