Question

How do you draw the line with the slope \[m = \dfrac{1}{2}\] and y-intercept 5?

Answer 1

Hint: First we need to find the equation of a line with slope and y-intercept. Since they have given the y-intercept and now we need to find the x-intercept. That is the coordinate of the given equation lying on the line of x- axis, we can find this by substituting the value of ‘y’ is equal to zero (x-intercept). We know that the y-intercept is coordinate of the equation lying on the line of y- axis if y-intercept is not given, we can find this by substituting the value of ‘x’ equal to zero (y-intercept).

Complete step-by-step solution:
Given slope \[m = \dfrac{1}{2}\] and y-intercept is 5.
We know that the equation of a line with slope ‘m’ and y-intercept ’c’ is,\[y = mx + c\].
Thus we have the equation
\[y = \dfrac{1}{2}x + 5\]
They have given the y-intercept is 5. In the coordinate form we have \[(0,5)\].
Now we need to find the x-intercept. To find the x-intercept substitute \[y = 0\] in \[y = \dfrac{1}{2}x + 5\]. That is
\[(0) = \dfrac{1}{2}x + 5\]
\[
  \dfrac{1}{2}x + 5 = 0 \\
  \dfrac{1}{2}x = - 5 \\
\]
Multiply 2 on both side of the equation we have,
\[
  x = - 5 \times 2 \\
  x = - 10 \\
\]
Thus we have the coordinate point which lies on the x-axis is \[( - 10,0)\]
Thus we draw the graph for the coordinates \[(0,5)\] and \[( - 10,0)\].

All we did was expand the line touching the points \[(0,5)\] and \[( - 10,0)\] by a straight line.
Without the calculation we have found few more points using the graph. The coordinate points are\[( - 8,1),( - 6,2),( - 4,3)\] and \[( - 2,4)\].

Note: A graph shows the relation between two variable quantities, it contains two axes perpendicular to each other namely the x-axis and the y-axis. Each variable is measured along one of the axes. In the question, we are given one linear equation containing two variables namely x and y, x is measured along the x-axis and y is measured along the y-axis while tracing the given equations.