Question

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 1

we know that

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

$y-y1=m*(x-x1)$

in this problem we have

$m=2\\point (x1,y1)=(0,3)$

substitute the values in the formula

$y-3=2*(x-0)$

$y=2x+3$

therefore

the answer is

$y=2x+3$

Answer 2

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

$\boxed{ \ Slope-intercept \ form: y = mx + c \ }$

Substitution.

$\boxed{ \ \ m = 2 \rightarrow y = 2x + c \ }$

$\boxed{ \ c = 3 \ } \rightarrow \boxed{ \ y = 2x + 3 \ }$

Thus the slope-intercept form is $\boxed{\boxed{ \ y = 2x + 3 \ }}$

Part-2

$\boxed{ \ Point-slope \ form: y - y_1 = m(x - x_1) \ }$

$\boxed{ \ m = 2 \rightarrow y - y_1 = 2(x - x_1) \ }$

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

$\boxed{ \ x_1 = 0, y_1 = 3 \ } \rightarrow \boxed{ \ y - 3 = 2(x + 0) \ }$

Thus the point-slope form is $\boxed{\boxed{ \ y - 3 = 2x \ }}$

Part-3

$\boxed{ \ Standard \ form: ax + by = k \ }$

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

$\boxed{ \ y = 2x + 3 \ }$

$\boxed{ \ 2x + 3 = y \ }$

$\boxed{ \ 2x - y = - 3 \ }$

Thus the standard form is $\boxed{\boxed{ \ 2x - y = - 3 \ }} \ or \ \boxed{\boxed{ \ 2x - y + 3 = 0 \ }}$

Learn more

1. Find out ordered pairs could be points on a line that is perpendicular to another line  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  brainly.com/question/1473992
3. The midpoint 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