Question

How do you find the slope and intercept to graph \[y=5x-9\]?

Answer 1

Hint: In this given problem, we have a line equation, in which we have to find the slope and intercepts, to plot the graph. We know that slope intercept form is \[y=mx+c\] where m is the slope and c is the y-intercept. By using the slope intercept formula, we can find the slope. We also know that for x-intercept the value of y is 0 and for y-intercept the value of x is 0. From these points, we can plot the graph.

Complete step by step answer:
We know that the given slope intercept form is,
\[y=5x-9\] ……… (1)
We also know that the general form of the slope intercept form is,
\[y=mx+c\] ……… (2)
Where, m is the slope and c, y-intercept.
Now we can compare equation (1) and (2), we get
Slope, m = 5 and y-intercept, c = -9
We also know that at y-intercept, x = 0.
Therefore, the point at y-intercept is \[\left( 0,-9 \right)\].
Now, we have to find the x-intercept.
We know that at x-intercept, y = 0. Substituting the value of y in equation (1), we get
\[\begin{align}
  & \Rightarrow 0=5x-9 \\
 & \Rightarrow x=\dfrac{9}{5}=1.8 \\
\end{align}\]
Therefore, the point at x-intercept is \[\left( 1.8,0 \right)\].
We can also find some other points to be plotted in the graph where the line passes through.
We can assume for x = 1, then from (1).
\[\begin{align}
  & \Rightarrow y=5\left( 1 \right)-9 \\
 & \Rightarrow y=-4 \\
\end{align}\]
Therefore, the other point is \[\left( 1,-4 \right)\].
Now we can plot the graph using x-intercept \[\left( 1.8,0 \right)\], y-intercept \[\left( 0,-9 \right)\] and the other point \[\left( 1,-4 \right)\].

Note:
Students make mistakes in finding the value of x-intercept and y-intercept, we should know that at x-intercept the value of y is 0 and at y-intercept the value of x is 0. We should also concentrate on formulae like slope intercept formulas, to solve these types of problems.