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 $$(0,-9)$$.
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
$$\begin{array}{rl}& \Rightarrow 0=5x-9\\ & \Rightarrow x={\displaystyle \frac{9}{5}}=1.8\end{array}$$
Therefore, the point at x-intercept is $$(1.8,0)$$.
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).
$$\begin{array}{rl}& \Rightarrow y=5\left(1\right)-9\\ & \Rightarrow y=-4\end{array}$$
Therefore, the other point is $$(1,-4)$$.
Now we can plot the graph using x-intercept $$(1.8,0)$$, y-intercept $$(0,-9)$$ and the other point $$(1,-4)$$.

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.