Answered

Nolan plots a point at (0, 3) on the y-axis. He uses a slope of 2 to graph another point. He draws a line through the two points. Which equation represents Nolan’s line?

Answer :

calculista

we know that

the equation of the line in the point -slope form is equal to

[tex]y-y1=m*(x-x1)[/tex]

in this problem we have

[tex]m=2\\point (x1,y1)=(0,3)[/tex]

substitute the values in the formula

[tex]y-3=2*(x-0)[/tex]

[tex]y=2x+3[/tex]

therefore

the answer is

[tex]y=2x+3[/tex]

BladeRunner212

y = 2x + 3 or 2x - y + 3 = 0.

Further explanation

We will help Nolan determine the straight-line equation he made. Later the equation will be arranged in slope-intercept, point-slope, and standard form.

Given:

  • Nolan plots a point at (0, 3) on the y-axis.
  • He uses a slope of 2 to graph another point.
  • He draws a line through the two points.

Question:

Which equation represents Nolan’s line?

The Process:

  • Slope or gradient m = 2
  • The y-intercept is (0, c), i.e., (0, 3)

Part-1

[tex]\boxed{ \ Slope-intercept \ form: y = mx + c \ }[/tex]

Substitution.

[tex]\boxed{ \ \ m = 2 \rightarrow y = 2x + c \ }[/tex]

[tex]\boxed{ \ c = 3 \ } \rightarrow \boxed{ \ y = 2x + 3 \ }[/tex]

Thus the slope-intercept form is [tex]\boxed{\boxed{ \ y = 2x + 3 \ }}[/tex]

Part-2

[tex]\boxed{ \ Point-slope \ form: y - y_1 = m(x - x_1) \ }[/tex]

[tex] \boxed{ \ m = 2 \rightarrow y - y_1 = 2(x - x_1) \ } [/tex]

The line passing through the point (0, 3).

[tex] \boxed{ \ x_1 = 0, y_1 = 3 \ } \rightarrow \boxed{ \ y - 3 = 2(x + 0) \ } [/tex]

Thus the point-slope form is [tex]\boxed{\boxed{ \ y - 3 = 2x \ }}[/tex]

Part-3

[tex]\boxed{ \ Standard \ form: ax + by = k \ }[/tex]

From the results of Part-1, we set the position of the variables.

[tex]\boxed{ \ y = 2x + 3 \ }[/tex]

[tex]\boxed{ \ 2x + 3 = y \ }[/tex]

[tex]\boxed{ \ 2x - y = - 3 \ }[/tex]

Thus the standard form is [tex]\boxed{\boxed{ \ 2x - y = - 3 \ }} \ or \ \boxed{\boxed{ \ 2x - y + 3 = 0 \ }}[/tex]

Learn more

  1. Find out ordered pairs could be points on a line that is perpendicular to another line  https://brainly.com/question/2601054
  2. Determine the line equation, in slope-intercept form, that is parallel to the given line and passes through a point  https://brainly.com/question/1473992
  3. The midpoint https://brainly.com/question/3269852

Keywords: Nolan, plots a point at (0, 3) on the y-axis, the equation, slope-intercept form, standard form, point-slope, gradien, parallel, perpendicular, passes, the y-intercept, constant, he draws a line through the two points

${teks-lihat-gambar} BladeRunner212

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