Question

How do you find the x intercepts of \[y = 2x + 5\] ?

Answer 1

Hint: Here in this question, we have to plot the graph for the equation. By substituting the x is equal to zero we can find the y intercept value and substituting y is equal to zero we can find the x intercept value. By equating the given equation to the general equation of line we can determine the slope. Here we have found the x intercepts.

Complete step-by-step answer:
 The given equation is in the form of \[y = mx + b\] , where m is slope and b is known as y-intercept. Slope means ratio of vertical change to the horizontal change i.e., ratio of change in y-axis or step size of y-axis to the change in x-axis or step size of x-axis. An intercept is a point where the straight line or a curve intersects the y-axis in a plane. If the point x is zero then the obtained point is a y -intercept.
Now consider the given equation \[y = 2x + 5\] -----------(1)
Substitute the value of y as 0 in the equation (1) then we have
 \[ \Rightarrow 0 = 2x + 5\]
On simplifying we get
 \[
   \Rightarrow - 5 = 2x \\
   \Rightarrow \dfrac{{ - 5}}{2} = x \\
   \Rightarrow x = - 2.5 \;
 \]
Therefore, x-intercept is (-2.5, 0)
We can also find the y- intercept
Substitute the value of x as 0 in equation (1), then we have
 \[ \Rightarrow y = 2(0) + 5\]
On simplifying we get
 \[ \Rightarrow y = 5\]
Therefore, y-intercept is (0, 5)
Hence we have found the x intercepts and also the y intercepts.
The graph for this is given below

Note: The question belongs to the concept of graph. By comparing the given equation to the equation of a line we calculate the slope and intercept. Or by choosing the value of x we can determine the value of y and then plotting the graphs for these points we obtain the result.