Question

How do you find the slope and intercept of \[y=5x+10\]?

Answer 1

Hint: This type of problem is based on the concept of equation of lines. First, we need to find the slope of the given equation by comparing it with slope-intercept form \[y=mx+c\]. Then, we have to find the intercepts of the given equation by making necessary calculations. We then have to make necessary calculations and compare with the intercept form of the line \[\dfrac{x}{a}+\dfrac{y}{b}=1\].
Thus, we get the slope and intercepts of the given equation \[y=5x+10\].

Complete step by step answer:
According to the question, we are asked to find the slope and intercept of the given equation.
We have been given the equation is \[y=5x+10\] -----(1)
Let us first find the slope.
We know that the slope-intercept form of the equation is \[y=mx+c\], where m is the slope.
Comparing (1) with \[y=mx+c\], we get,
m=5
Therefore, the slope of the equation \[y=5x+10\] is 5.
Now, let us find the intercepts of the equation \[y=5x+10\].
\[\Rightarrow y=5x+10\]
Let us add -5x on both sides of the equation.
\[\Rightarrow y-5x=5x-5x+10\]
\[\Rightarrow y-5x=10\]
Now divide 10 on both the sides of the equation. We get,
\[\Rightarrow \dfrac{y-5x}{10}=\dfrac{10}{10}\]
\[\Rightarrow \dfrac{y}{10}-\dfrac{5x}{10}=1\]
\[\Rightarrow \dfrac{y}{10}-\dfrac{x}{2}=1\]
\[\therefore \dfrac{x}{\left( -2 \right)}+\dfrac{y}{10}=1\] -------(2)
Compare equation (2) with the intercept form of a line, that is, \[\dfrac{x}{a}+\dfrac{y}{b}=1\].
Here, a is the x-intercept and b is the y-intercept.
Therefore, the intercepts of the given equation is \[y=\dfrac{4}{5}x+5\] are
x-intercept is -2 and y-intercept is 10.
Hence, the slope of the given equation \[y=\dfrac{4}{5}x+5\] is 5 and the intercepts of ‘x’ and ‘y’ are -2 and 5 respectively.

Note:
Whenever you get this type of problems, we should try to make the necessary calculations in the given equation to get the slope intercept form and intercept form to find the slope and intercepts. We should avoid calculation mistakes based on sign conventions. We can also convert the equation directly by cross multiplying the equation. Then make some necessary calculations to obtain the final answer.