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
- Find out ordered pairs could be points on a line that is perpendicular to another line https://brainly.com/question/2601054
- 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
- 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
