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# In the xy-plane, ﬁnd the following. (a) Slope and y-intercep

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In the xy-plane, ﬁnd the following. (a) Slope and y-intercep [#permalink]  24 May 2019, 08:13
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In the xy-plane, ﬁnd the following.

(a) Slope and y-intercept of the line with equation 2y+x=6

(b) Equation of the line passing through the point (3,2) with y-intercept 1

(c) The y-intercept of a line with slope 3 that passes through the point (−2,1)

(d) The x-intercepts of the graphs in (a), (b), and (c)

[Reveal] Spoiler: OA
(a) Slope: $$- \frac{1}{2}$$; y-intercept:; 3 (b) $$y=\frac{x}{3}+1$$ (c) 7 (d) $$6,-3, - \frac{7}{3}$$

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Re: In the xy-plane, ﬁnd the following. (a) Slope and y-intercep [#permalink]  27 May 2019, 13:09
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Carcass wrote:
In the xy-plane, ﬁnd the following.

(a) Slope and y-intercept of the line with equation 2y+x=6

(b) Equation of the line passing through the point (3,2) with y-intercept 1

(c) The y-intercept of a line with slope 3 that passes through the point (−2,1)

(d) The x-intercepts of the graphs in (a), (b), and (c)

[Reveal] Spoiler: OA
(a) Slope: $$- \frac{1}{2}$$; y-intercept:; 3 (b) $$y=\frac{x}{3}+1$$ (c) 7 (d) $$6,-3, - \frac{7}{3}$$

It's often useful to take the equation of a line and rewrite it slope y-intercept form y = mx + b, where m is the line's slope, and b is the line's y-intercept.

(a) Slope and y-intercept of the line with equation $$2y + x = 6$$

Take: $$2y + x = 6$$

Subtract x from both sides: $$2y = -x + 6$$

Divide both sides by 2 to get: $$y = -\frac{1}{2}x + 3$$

We can see that the slope is $$-\frac{1}{2}$$, and the y-intercept is 3
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(b) Equation of the line passing through the point (3,2) with y-intercept 1

If the y-intercept is 1, then $$b = 1$$

So, far we have: $$y = mx + 1$$

Since the point (3,2) lies ON the line, it's coordinates (x = 3 and y = 2) must SATISFY the equation of the line.

Replace values to get: $$2 = m(3) + 1$$

Subtract 1 from both sides to get: $$1 = 3m$$

Solve: $$m = \frac{1}{3}$$

The equation of the line is $$y = \frac{1}{3}x + 1$$
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(c) The y-intercept of a line with slope 3 that passes through the point (−2,1)

If the slope is 3, then $$m = 3$$

So, far we have: $$y = 3x + b$$

Since the point (−2,1) lies ON the line, it's coordinates (x = -2 and y = 1) must SATISFY the equation of the line.

Replace values to get: $$1 = 3(-2) + b$$

Simplify: $$1 = -6 + b$$

Solve: $$b = 7$$

So, the y-intercept is 7

By the way, the equation of the line is $$y = 3x + 7$$
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(d) The x-intercepts of the graphs in (a), (b), and (c)
Key concept: the x-intercept is the x-value when y = 0

So, for each equation, replace y with 0 and solve for x.

a) Replace y with 0 to get: $$0 = -\frac{1}{2}x + 3$$

Subtract 3 from both sides: $$-3 = -\frac{1}{2}x$$

Solve: $$x = 6$$

The x-intercept is 6

b) Replace y with 0 to get: $$0 = \frac{1}{3}x + 1$$

Subtract 1 from both sides: $$-1 = \frac{1}{3}x$$

Solve: $$x = -3$$

The x-intercept is -3

c) Replace y with 0 to get: $$0 = 3x + 7$$

Subtract 7 from both sides: $$-7 = 3x$$

Solve: $$x = -\frac{7}{3}$$

The x-intercept is $$-\frac{7}{3}$$

Cheers,
Brent
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Brent Hanneson – Creator of greenlighttestprep.com

Re: In the xy-plane, ﬁnd the following. (a) Slope and y-intercep   [#permalink] 27 May 2019, 13:09
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